A hat-trick from striker Chris Simm gave Leigh just the tonic they needed after Saturday's disappointing 3-0 defeat at home to Barow.
The Railwaymen gave a much-improved display to earn three points they desperately needed in their fight to avoid the drop from the Conference North.
Simm gave RMI a 20th-minute lead, but despite the setback of conceding a penalty, through Tony Filipek, just on the stroke of half-time which Richard Forster duly dispatched, the home side came out after the break and outplayed the Spartans.
And Railwaymen forward struck twice more, in the 57th and 64th minutes, to complete a memorable treble and seal a vital win for Stuart Humphries men.
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