The fans had to wait 40 minutes for the first goal when a driven cross from Max Gradel on the left wing went into the net via Grimsby defender Olly Lancashire.
But in first half injury time Leeds added a second as midfielder Neil Kilkenny played a one-two on the edge of the box with Jermaine Beckford and planted a well placed shot into the bottom corner of the net.
If Grimsby were unlucky to be two down at the break after a lively, committed performance they were definitely hard done to when the hosts scored a third time 10 minutes into the second period.
Bradley Johnson surged forward from his central midfield position and found Beckford in the box, the United number nine then did the rest, although he did not make clean contact as the ball rolled into the net rather than broke the back of it.
Grimsby immediately hit back when they forced a corner and from it Casper Ankergren's punch was met by a stunning volley from former Leeds player Peter Sweeney.
The spectacular effort went in off the crossbar to enable him to celebrate his first return to Elland Road since his summer move with a goal.
The visitors remained in the contest right up to the final whistle, but they only created one further decent chance when Ankergren came out well to block a shot from Bradley Wood when he had raced clear after taking the ball off young left back Aidan White.
At the other end, Grimsby keeper Nick Colgan pushed a Robert Snodgrass close range header onto the post.
Gradel hit the side netting with an angled shot and substitute Andy Robinson sent several efforts just wide from the edge of the box.
In the first half Sam Vokes had headed over from good positions twice and Kilkenny gave Grimsby warning of his shooting ability with two good efforts before he got his deserved goal.
Overall Leeds did enough to earn the win, but elements of their play were sloppy and they will have to play better in this competition in future if they are to reach Wembley.
They have been joined in the northern area semi-finals by Carlisle, Accrington Stanley and Bradford City.
Match facts: Leeds United 3 (Lancashire og 40, Kilkenny 45, Beckford 55) Grimsby Town 1 (Sweeney 57) Att: 10,430
United: Ankergren, Hughes, Naylor, Michalik, White, Gradel, Johnson (Prutton 81), Kilkenny, Snodgrass (Robinson 67), Vokes (Showunmi 86), Beckford.
Town: Colgan, Bore, Lancashire, Atkinson, McCrory, Clarke (Wood 77), Leary, Sweeney, Shahin, North (Akpro), Forbes (Conlon 67).
Referee: Neil Swarbrick.