Goals from Matty Sargent and Scott Duxbury put the Blues in control at half-time, before Sargent scored his second of the match with 15 minutes remaining to wrap up the win.
That was Rylands' first away win under Michael Clegg, and also their third league victory in a row.
As for Radcliffe, they missed the chance to consolidate their play-off spot and remain just two points ahead of Hyde United in the fight for the final top-five spot, with Matlock Town one point further back.
Tuesday's fixture at the Neuven Stadium was originally scheduled for Easter Monday but was postponed due to a waterlogged pitch.
Results - Tuesday 11 April
Radcliffe 0-3 Warrington Rylands
Photo credit: Warrington Rylands
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