Connor Woods opened the scoring at the Neuven Stadium shortly before the hour mark. Then following Radcliffe forward Jude Oyibo's late red card for a challenge on Tom Hannigan, the Yellows capitalised as Isaac Buckley-Ricketts and Josh Amis sealed the points in the closing stages.
Further down the division, it proved to be a difficult night for Belper Town as their relegation from the Northern Premier League was confirmed.
The Nailers were beaten 1-0 by Marske United, with top scorer Adam Boyes firing the Seasiders out of the relegation zone.
Elsewhere, second-placed Bamber Bridge kept up the pressure on league leaders South Shields as Connor Thomson's early strike saw them past struggling Morpeth Town at the Sir Tom Finney Stadium.
Liversedge also kept their hopes of surviving the drop alive as Nathan Carman scored a 90th minute equaliser to rescue a 1-1 draw at home to Lancaster City.
And finally, Matlock Town kept their play-off hopes alive with an enthralling 3-2 victory over Marine.
The result saw the Gladiators climb level on points with their opponents in the Northern Premier League table after they came from behind to win a topsy-turvy affair.
Results - Tuesday 4 April
Bamber Bridge 1-0 Morpeth Town
Belper Town 0-1 Marske United
Liversedge 1-1 Lancaster City
Matlock Town 3-2 Marine
Radcliffe 0-3 Warrington Town
Photo credit: Sean Walsh
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