The Reds moved to within a point of Institute after winning this JJB Sports Premiership mid-table encounter.
Cliftonville striker Chris Scannell had an early shot saved before he netted from close-range on 43 minutes.
Barry Holland's shot was cleared off the line by Institute's Ryan Semple while Aaron Smyth struck the crossbar.
Smyth smashed in from six yards to make it 2-0 after 63 minutes before Reds keeper John Connolly denied Sean Friars and Paul Brown.
Connolly also kept out Institute in the first half with a save from Austin Friel's shot.
Scannell pounced to score after Mark Patterson flicked on from Mark Holland's cross.
Smyth doubled the lead with the full-back smashing in after Institute failed to clear from a corner.
Eddie Patterson's team stay seventh but they have a game in hand on Institute.
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