A penalty from Lee Hughes was enough to give Rolland Nilsson's side the three points that takes them within three points of leaders Crystal Palace.
The only goal of the game came on the half hour when a poor clearance from Crewe goalkeeper Ade Bankole went straight to Youseff Safri who drove into the box before being bundled over by defender Efe Sodje.
The Sky Blues's £5 million summer signing from West Brom stepped up to slot home the kick despite Bankole going the right way diving low to his left.
The goal was Hughes's first goal in a month and just his third goal of his injury-hit career at Coventry.
Despite a brave showing from Dario Gradi's side, they failed to emulate their impressive away win at Wolves and remain in 16th spot in the league.
