A goal by former Leeds striker Antony Elding took the game into extra-time, where United duly went on a scoring spree.
Substitutes Mike Grella (twice), Tresor Kandol, and Jermaine Beckford all found the net to spare the home side's blushes and avoid the lottery of a penalty shoot-out.
The final scoreline was harsh on the Blue Square Premier side who had been only 12 minutes away from victory in the original tie at Rockingham Road nine days ago.
Leeds had failed to build on an early lead provided by Lucianno Becchio and put their supporters through a nail-biting night.
Now, however, they can look forward to a reunion with the club their supporters love to hate, the first meeting since Leeds were relegated from the Premier League five years ago.
Chairman Ken Bates believes next month's tie at Old Trafford is worth around £750,000 to Leeds taking into account gate receipts, television money, and a £27,000 prize for reaching the third round.
But it could so easily have been the minnows from the Blue Square league heading to the so-called 'Threatre of Dreams.'
Leeds dominated the opening stages but always knew that Kettering could grow in confidence the longer the game stayed goalless.
Becchio, however, helped settle the nerves in the 20th minute, rising above his marker to head home a Robert Snodgrass cross.
"Are you watching, Manchester?" chanted the Leeds fans. Probably not was the answer to that question considering the Red Devils were in Champions League action against Wolfsburg on another channel.
Leeds had plenty of opportunities to increase the lead. Beckford had a low shot saved by Harper and then flicked a header wide from six yards out, Neil Kilkenny's 35-yard drive hit the foot of the post.
Given the balance of play, Leeds's failure to score again before the interval could only have been a massive disappointment to those fans who had braved the rain and paid £15 or over to attend instead of watching at home on ITV4.
Kettering threatened only once before the break when Elding blazed a half-chance over the bar when under pressure from Leigh Bromby.
Player-manager Harper, 38, the hero for Kettering at Rockingham Road, was again standing up to the Leeds attack.
The veteran goalkeeper, an Arsenal reserve in his younger days, rode his luck, however, when a Becchio header hit the post and struck him in the chest just after the break.
Harper should really have been picking the ball out of the net given the space Becchio had been afforded.
Becchio was making his first start in over two months for Leeds but manager Simon Grayson had resisted the temptation to make wholesale changes aware of the importance of victory.
Becchio, fit again after ankle trouble, replaced on-loan Sam Vokes who was ineligible along with Max Gradel, Hogan Ephraim and David Martin.
Kettering's side contained only one change from the original tie; striker Kithson Bain replacing Moses Ashikodi.
Elements of complacency had crept into the Leeds's game before Elding struck his equaliser.
The on loan Kettering striker spent just six months on the books at Elland Road after being signed from Stockport County by Dennis Wise.
He made only nine appearances and scored one goal before being released by Gary McAllister two summers ago.
The striker stunned the majority of the 10,673 crowd just after the hour mark with a close-range header in front of the South Stand.
When things started to look critical, Grayson ripped into his players from the touchline.
Leeds stepped it up a gear but Harper's luck held out when he spilled a low drive from Kilkenny only for the ball to roll wide of the post.
With greater care, Leeds would have avoided extra-time but, too often, players opted for personal glory rather than an unselfish pass and the chance was lost.
Kettering also had Andre Boucaud to thank for a goalline clearance in the final seconds of normal time which kept out a header from Tresor Kandol.
Snodgrass hit the woodwork at the start of extra-time as Leeds' frustrations mounted. By the end, it looked like it had been a doddle - but nothing was further from the truth.
Leeds United: Ankergren; Hughes (Grella 105), Bromby, Michalik, White (Capaldi 56); Snodgrass, Howson, Doyle, Kilkenny; Becchio (Kandol 76), Beckford.
Subs Unused: A.Martin, Crowe, Marques, Prutton.
Kettering Town: Harper; Taylor, Dempster, Roper, Davis; Noubissie (Fowler 105), Heslop Boucaud; Partridge (Wrack 96); Elding, Bain (Thomas h/t).
Subs Unused: Bussey, Cooper, Cherry.
Referee: PT Crossley (Kent).
Substitutes Mike Grella (twice), Tresor Kandol, and Jermaine Beckford all found the net to spare the home side's blushes and avoid the lottery of a penalty shoot-out.
The final scoreline was harsh on the Blue Square Premier side who had been only 12 minutes away from victory in the original tie at Rockingham Road nine days ago.
Leeds had failed to build on an early lead provided by Lucianno Becchio and put their supporters through a nail-biting night.
Now, however, they can look forward to a reunion with the club their supporters love to hate, the first meeting since Leeds were relegated from the Premier League five years ago.
Chairman Ken Bates believes next month's tie at Old Trafford is worth around £750,000 to Leeds taking into account gate receipts, television money, and a £27,000 prize for reaching the third round.
But it could so easily have been the minnows from the Blue Square league heading to the so-called 'Threatre of Dreams.'
Leeds dominated the opening stages but always knew that Kettering could grow in confidence the longer the game stayed goalless.
Becchio, however, helped settle the nerves in the 20th minute, rising above his marker to head home a Robert Snodgrass cross.
"Are you watching, Manchester?" chanted the Leeds fans. Probably not was the answer to that question considering the Red Devils were in Champions League action against Wolfsburg on another channel.
Leeds had plenty of opportunities to increase the lead. Beckford had a low shot saved by Harper and then flicked a header wide from six yards out, Neil Kilkenny's 35-yard drive hit the foot of the post.
Given the balance of play, Leeds's failure to score again before the interval could only have been a massive disappointment to those fans who had braved the rain and paid £15 or over to attend instead of watching at home on ITV4.
Kettering threatened only once before the break when Elding blazed a half-chance over the bar when under pressure from Leigh Bromby.
Player-manager Harper, 38, the hero for Kettering at Rockingham Road, was again standing up to the Leeds attack.
The veteran goalkeeper, an Arsenal reserve in his younger days, rode his luck, however, when a Becchio header hit the post and struck him in the chest just after the break.
Harper should really have been picking the ball out of the net given the space Becchio had been afforded.
Becchio was making his first start in over two months for Leeds but manager Simon Grayson had resisted the temptation to make wholesale changes aware of the importance of victory.
Becchio, fit again after ankle trouble, replaced on-loan Sam Vokes who was ineligible along with Max Gradel, Hogan Ephraim and David Martin.
Kettering's side contained only one change from the original tie; striker Kithson Bain replacing Moses Ashikodi.
Elements of complacency had crept into the Leeds's game before Elding struck his equaliser.
The on loan Kettering striker spent just six months on the books at Elland Road after being signed from Stockport County by Dennis Wise.
He made only nine appearances and scored one goal before being released by Gary McAllister two summers ago.
The striker stunned the majority of the 10,673 crowd just after the hour mark with a close-range header in front of the South Stand.
When things started to look critical, Grayson ripped into his players from the touchline.
Leeds stepped it up a gear but Harper's luck held out when he spilled a low drive from Kilkenny only for the ball to roll wide of the post.
With greater care, Leeds would have avoided extra-time but, too often, players opted for personal glory rather than an unselfish pass and the chance was lost.
Kettering also had Andre Boucaud to thank for a goalline clearance in the final seconds of normal time which kept out a header from Tresor Kandol.
Snodgrass hit the woodwork at the start of extra-time as Leeds' frustrations mounted. By the end, it looked like it had been a doddle - but nothing was further from the truth.
Leeds United: Ankergren; Hughes (Grella 105), Bromby, Michalik, White (Capaldi 56); Snodgrass, Howson, Doyle, Kilkenny; Becchio (Kandol 76), Beckford.
Subs Unused: A.Martin, Crowe, Marques, Prutton.
Kettering Town: Harper; Taylor, Dempster, Roper, Davis; Noubissie (Fowler 105), Heslop Boucaud; Partridge (Wrack 96); Elding, Bain (Thomas h/t).
Subs Unused: Bussey, Cooper, Cherry.
Referee: PT Crossley (Kent).