Third-bottom Club have only won once to date this season, while Leek have been inconsistent. It was goalless at the break before Tim Grice gave the Blues the lead just two minutes into the second period.
Ten minutes later and Daniel Trickett-Smith, recently signed from American side Sacremento Republic, doubled the hosts' lead. He added his second and Leek's third on 68 minutes to seal the points.
Corby Town, relegated from the Premier Division at the end of last season, are only a point above Sheffield after losing 2-1 at Chasetown, finishing the game with only nine-men.
The Steelmen were up against it pretty much from the start as goalkeeper Paul Bastock was sent-off after just five minutes for bringing down Muzzy Nduna just outside the box. Chasetown eventually broke the deadlock on the stroke of half-time when Will Whieldon followed up to score after his first effort hit the post.
The Scholars` advantage was doubled seven minutes into the second half when Nduna scored but the Steelmen pulled a goal back from sub Sam Warburton in the 72nd minute. However, their hopes were effectively dashed when Jason Lee was shown a straight red card for bringing down Nduna when he was in on goal.
Tuesday`s other game saw Market Drayton Town and Loughborough Dynamo share a 2-2 draw in Shropshire.
Dynamo had a great start when Ashley Hodgkinson put them in front after less than a minute but Dan Beddowes replied 18 minutes later. Glynn Coney then gave the hosts the lead nine minutes after the break, a lead they held until nine minutes from time when Josh Riley equalised.
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