But the rebel Reds, who were desperate to bounce back from their agonising last-gasp defeat at Witton, had to wait until two minutes from time to secure the win.
Jamie Baguley was on hand to clinch their fourth victory in five games with a 25-yard screamer.
Jerome Wright had given United a 15th minute lead when he drilled home from just inside the box.
But, despite dominating throughout, Karl Marginson's men were unable to kill off plucky Genesis, who were playing for the first time at their new Leigh Sports Village ground, until Baguley finally settled the issue with time running out.
The win takes United to within a point of a play-off place ahead of Saturday's crunch home clash with fellow promotion contenders Guiseley.
Meanwhile, Altrincham played out their second Blue Square Premier draw in four days as they were held 1-1 by York at Moss Lane.
The Robins led at the break through Shaun Densmore's 15th minute goal, but Richard Brodie equalised within a minute of the re-start to earn the visitors a point.
Relegation-haunted Northwich remain anchored at the foot of the table despite ending their six-match losing streak with a thrilling 3-3 draw at Wrexham.
Droylsden's hopes of forcing their way into the Blue Square North promotion picture suffered a set-back in a 1-0 disappointing defeat at Gainsborough.
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F C JOHN, LADYBARN (28/01/2009 at 15:53)
I'm sure all fellow FC fans will have enjoyed the outing to Leigh's superb new stadium. No doubt many were thinking, like me, that such a set-up would be ideal for FC. It was such a shame though, that the 1,300 crowd only seemed to include - at most - around 200 locals. Such poor support at the opening of such a cracking new venue was really sad. Good job it was FC they were playing. We can guarantee any club their best gate of the season.