Gary McAllister's call for a repeat of the siege mentality which characterised their superb start to last season was quickly answered with a fine victory over a team who are also favourites to bounce back after relegation.
The United boss handed debut starts to three summer signings in Andy Robinson, Enoch Showunmi and Robert Snodgrass, while striker Luciano Becchio made a brief cameo appearance from the bench.
The Iron were without new recruit from York City, Martyn Woolford, due to an eye injury.
Despite falling behind to Gary Hooper's 57th-minute goal, United refused to buckle and their resilience was rewarded with goals by strikers Showunmi and Jermaine Beckford as winger Snodgrass became an instant hit with the fans.
Snodgrass, signed from Livingston, was full of energy and ideas. He also gave the side much-needed width and was the victim of the officials' failure to spot the ball crossing the line just before half-time.
The Scot's gentle effort was amazingly dropped by 'keeper Josh Lillis. The ball ran through his legs and seemed to cross the line before he clawed it back but neither the referee nor his assistant saw the incident clearly.
Scunthorpe began the game strongly, closing Leeds down in midfield and winning a series of free-kicks, but the Whites defended well, often catching Hooper, a £175,000 summer capture from Southend United, offside.
After Grant McCann had wasted a good chance for the Iron, Leeds finished the first half in the ascendancy as Showunmi shot just wide, Beckford hit the side-netting and Snodgrass suffered the frustration of that 'goal'.
Leeds were still on top when Scunthorpe shocked them by taking the lead, Hooper punishing a slip-up by Rui Marques.
But Scunthorpe's lead lasted just four minutes before Showunmi was fouled by Kenny Milne. The resultant free-kick by Snodgrass was headed down into the corner by Showunmi from 12-yards.
With Snodgrass growing in confidence in his first competitive game since crossing the border, Beckford brought a good save from Lillis before scoring against the club where he spent nearly four months on loan the season before last.
David Prutton's powerful shot came back off the bar and Beckford knocked in the rebound to give his side the lead.
Becchio replaced Showunmi with nine minutes left and the Argentinian almost marked his debut with a spectacular goal, his stunning left-foot drive forcing another excellent save from Lillis.
The experienced Paul Telfer, who has signed on a non-contract basis, was left on the bench but could have an important part to play as the season progresses.
Prutton, who took up some good scoring positions, should have added a third Leeds goal but missed when it seemed easier to score just before the end.
Frazer Richardson captained the side as Leeds maintained their record of avoiding defeat on the season's opening day since their last reverse in 1989.
United now visit Chester on Tuesday night in the Carling Cup first round.