A superb goal from Laurence Wilson gave the Shrimps their third successive win.
Wilson scored with a stunning individual effort on 24 minutes after he waltzed his way past several weak Cheltenham challenges to slot the ball past Scott Brown.
From there Brown saved well from a long range Michael Twiss effort and Phil Jevons had a shot deflected wide after a last gasp challenge from Kyle Haynes.
Jevons then somehow managed to stop a Twiss corner from going in the Cheltenham net before Twiss tested Brown from long range at the end of the first half.
Cheltenham fought back in the second period with the wind behind them but only threatened briefly with Andy Parrish producing a superb goal lone clearance.
Morecambe: Roach; Hunter, Artell, Haining, Parrish, Wilson; Craney, Stanley, Twiss; Jevons, Mullin. Subs: Davies, Moss, Adams, Curtis, Wainwright, Duffy, McStay.
Cheltenham: Brown; Haynes, Gallinagh, Diallo, Low; Pook, Bird, Labadie; Lewis, Richards, Marshall. Subs: Perry, Hutton, Hammond, Watkins, Quaynor, Hayles, Alsop.
Ref: A Bratt.