The Shrimps got off to the perfect start with Rhys Turner marking his debut with a fine goal after just eight minutes.
A Crewe attack broke down and the Shrimps broke quickly with summer signing Turner, making his first full start, racing down on goal and beating Ben Garratt with a superb right-foot strike from just inside the area.
The Shrimps were lifted by the early goal and looked threatening going forward but were rocked by a Crewe equaliser on 22 minutes.
Ryan Lowe found himself in space down the right and saw his low cross diverted goalwards by Alex Kiwomya.
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Barry Roche did well to save the first effort but the Chelsea loanee reacted sharply to blast home the rebound from close range.
Jim Bentley’s side hit back with Cole Stockton forcing Garratt into an excellent low save with a shot from the edge of the area and heading narrowly over before the home side added a second after 42 minutes.
Again the Shrimps were left exposed down the right and Oliver Turton’s low cross was deflected past Roche by midfielder James Jones, who got in front of Liam Wakefield to beat Roche from six yards.
The second half saw few chances with the closest the Shrimps coming to a leveller being a Peter Murphy shot well saved by Garratt.
Stockton tried his luck several times from distance and Aaron Wildig saw an effort creep inches wide.
At the other end Crewe went close themselves on several occasions with Callum Saunders missing the target from close range and Ryan Lowe wasting a late chance but the home side held on for the win.
Crewe: Garratt, Turton, Davis, Guthrie, Ng, Cooper (Wintle 88), Jones, Hollands Kiwomya (Lowery 74), Dagnall (Saunders 78), Lowe. Subs not used: Richards, Nugent, Udoh, Wintle, Sinley
Morecambe: Roche, Wakefield, Edwards, Jennings, McGowan, Murhy, Wildig (Ellison), Rose, Conlan (Molyneux), Stockton, Turner (Mullin 75) Subs not used: Nizic, Hedley, Jordan
Ref: T Kettle
Attendance: 2, 844