The Sky Blues have made it three wins in seven days thanks to a first strike from Duckens Nazon.
The Haiti international's close range effort proved to t he be the difference between the two sides at the Ricoh as City close the gap on the automatic promtion places in SkyBet League Two.
Jodi Jones got the game's only assist after reacting quickest to a ball kept in play by the corner flag as Mark Robins' side make it nine points in seven days.
The game's opener came with a huge stroke of fortune. ones gambled on a ball that looked certain to be heading behind for a goal-kick until it was kept in play by the corner flag. Jones was then in and behind to charge across the byline and into the area where he picked out Nazon to fire home from close range. The Sky Blues had the luckiest of leads.
The goal had shaken the visitors and the following fifteen minutes was simply a Coventry onslaught. Jones came closest to doubling the lead two minutes later but his 25-yard curler came back off the crossbar.
After the inverval, the Railwaymen began to grow into the game. Former Sky Blue loanee Chris Dagnall came close to picking out Chris Porter with a low cross on the hour mark but Lee Burge was quick to pounce on that.
Brad Walker had looked like one of Crewe's better players over the afternoon and he too came close to pulling the visitors level. His free-kick from wide clipped the top of the cross bar as it arrowed over the bar.
Stuart Beavon has missed the last two games with a back injury and almost made an instant impact after coming on in the 72nd minute. The former Burton man turned his marker well to play Nazon in on goal but Alex 'keeper Dave Richards did well to deny Duckens his second.
The change gave City some life in the closing periods. Rod McDonald's effort from long range forced a strong double-save again from Richards with Nazon's rebound also being palmed away. The last action of the afternoon.
Yellows: Lowery 46',
Goals: Nazon 10',
Coventry City XI: Burge; Grimmer, Willis, McDonald, Stokes, Kelly, Doyle (C), Jones, Nazon, Dev. Kelly-Evans, Biamou (Beavon 72').
Subs: O'Brien, McNulty, Davies, Di. Kelly-Evans, Shipley, Stevenson.
Crewe Alexandra XI: Richards; Ng, Bakayogo, Walker (Grant 76'), Raynes, Porter, Dagnall (C), Bowery (Kirk 76'), Nolan, Ainley (Cooper '45), Lowery.
Subs: Garratt, Pickering, Dale, Reilly.