Max Clayton scored the winner midway through the first-half to return Crewe Alexandra back onto the victory trail at Gresty Road.
The teenager took advantage of good combination work between AJ Leitch-Smith and Gregor Robertson to expertly slot in his third goal of the campaign.
Coventry later went close as Cody McDonald struck the crossbar but the Alex held on for an excellent maximum points haul against opponents who were a couple of divisions higher than them last season.
Abdul Osman was recalled into midfield following the departure of skipper Ashley Westwood to Aston Villa – with Luke Murphy taking over the armband.
Former Stockport County midfielder Carl Baker missed an early opportunity for the visitors when he couldn’t get his header on target. He also drilled a later effort straight at goalkeeper Alan Martin.
But it was the hosts going into the lead when Leitch-Smith exchanged passes with the advancing Robertson and set-up Clayton to finish low past Joe Murphy.
Byron Moore then lacked sufficient force after a strong break from Luke Murphy and his shot rather drifted through to Joe Murphy, who was though required to gather from Crewe’s on loan striker Harry Bunn.
The visitors came out strongly after the break and McDonald struck the woodwork with a fine attempt while substitutes Gary McSheffrey and David McGoldrick were next to threaten. But Martin saved from the former and his colleague narrowly missed the target.
Crewe also had to survive a late scramble inside their own area before Moore failed to seriously trouble Joe Murphy at the other end as his side kept hold of their narrow advantage.
Crewe Alexandra: Martin, Mellor, Davis, Ellis, Robertson, Murphy, Osman, Clayton, Leitch-Smith, Moore, Bunn (Tootle 73)
subs (unused): Garratt, Dugdale, Turton, Guthrie, Daniels, West
Goals: Clayton (24)
Coventry City: Murphy, Clarke, Hussey, Edjenguele, Brown, Baker, Jennings (McSheffrey 66), Kilbane, Barton, McDonald (McGoldrick 59), Elliott (Ball 79)
subs (unused): Dunn, Christie, Wood, O’Donovan
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