Leeds saw off Grimsby to advance to the Northern Section semi-finals of the Johnstone's Paint Trophy.
The home side took the lead after 40 minutes when Olly Lancashire turned Max Gradel's cross into his own net.
Neil Kilkenny made it 2-0 in first-half injury time, firing home from the edge of the box to round off a neat move.
Jermaine Beckford slotted home Leeds' third after Bradley Johnson's fine run before Peter Sweeney hit a consolation for Grimsby with a well-taken volley.
Leeds United manager Simon Grayson told BBC Radio Leeds:
"Obviously delighted that we got the result and the performance was OK.
"I thought we played some decent stuff at times and we scored the goals at the right time which gave us the luxury to see the game through.
"We applied ourselves well, we worked hard - lacked a bit of quality in the final third at times - but we did enough to win the game."
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