The Bees dominated the first half but after Izale McLeod's strike was disallowed for offside the Shrimps took the lead three minutes before the break through Ellison. Former Manchester City youngster Redshaw marked his full Morecambe debut with a first goal for the club just after the hour to seal the points and leave Barnet two points above the drop zone.
With 12 minutes on the clock McLeod was felled on the edge of the box and Mark Byrne's free-kick was superbly saved by visiting goalkeeper Barry Roche.
Barnet thought they had gone ahead in the 25th minutes when a surging Ricky Holmes run and cross was slotted home by McLeod, only to be flagged offside.
Against the run of play Morecambe took the lead in the 42nd minute after Michael Hector lost the ball and Stewart Drummond's shot was spilled by Liam O'Brien, allowing top-scorer Kevin Ellison to collect his 17th of the season.
Morecambe doubled their lead in the 63rd minute when Redshaw smashed in Garry Hunter's cross before Lewis Alessandra hit the bar as the Shrimps threatened a third.
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