A Ciaran Kilheeney penalty a minute before the break settled nerves and the Wire confirmed victory with a second from Steven Gillespie 11 minutes from time.
Second-placed Spennymoor Town look determined to chase Warrington as far and for as long as possible after they hammered beleaguered New Mills 9-0, overhauling the leaders` goal difference by one in the bargain.
It was 6-0 at half-time with Nathan Fisher helping himself to a hat-trick and Mark Anderson, Liam Henderson and a Jon Rand own goal. Fisher added a personal fourth and before a Joe Tait penalty and Glen Taylor netted. The Millers go down with a goal difference already minus 115.
Third-placed Glossop North End`s game at Bamber Bridge was off, as was Burscough`s at Radcliffe Borough, leaving Northwich Victoria to move above them into fourth after a 5-2 win at home against Prescot Cables.
Stuart Cook and Scott Duxbury had Vics two-up by the 17th minute. Rob Doran pulled one back just before the break, but James Ball, Gary Burnett and a Michael Clarke spot-kick completed Northwich`s nap hand, with James Edgar adding a second for Cables near the end.
Clitheroe missed the chance to overtake Burscough when they were beaten 3-1 at home by an Ossett Albion side whose own top five hopes are still just about alive.
Connor Brunt gave Albion an eighth minute lead and then Rob Bordman netted a `hat-trick` - levelling with an own goal on 26 minutes and then scoring two at the right end, after 35 minutes from the spot and then in injury-time at the end of the game.
Trafford are six points adrift of the top five with only four games remaining but they beat Farsley Celtic 3-0 at home to keep hopes just about alive.
Liam Davies broke the deadlock after 68 minutes and an Aaron Burns brace on 81 and 90 minutes completed Trafford`s victory.
Harrogate Railway Athletic`s status is still just about alive, but a 2-1 defeat at Ingfield against the team immediately above them, Ossett Town, will not have helped morale.
Town have an eight-point cushion, thanks to Danny Frost after 20 minutes and Simon Rogers 12 minutes from time after Amar Purewal had levelled on 35 minutes.
Inconsistent Witton Albion won 3-2 at Queensgate against Scarborough Athletic with Rob Hopley bagging a brace, sandwiched by an Alex Titchiner effort – Jamie Forrester and Glenn Matthews replying, while Droylsden won 1-0 at Kendal Town, thanks to Shaquille Antoine-Clarke`s 55th minute effort.
Elsewhere, Mossley AFC beat Lancaster City 2-0 at Seel Park with a Dougie Carroll double on 41 and 45 minutes.
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