Midfielder Kenny Lunt was on hand to provide the crosses for Billy Jones and Madjid Bougherra to give the Railwaymen a 2-0 lead.
Stern John headed one back for the Sky Blues but Luke Rodgers lashed home to re-instate Crewe's two-goal cushion.
Gareth Taylor then completed the victory when he turned in Steve Jones' long-range effort.
Coventry boss Micky Adams:
"We can only apologise to the fans for our away results and I think I know why it is happening.
"The players understand my thoughts but I am not going to air them in public.
"I am not going to have a go at the players because they have been excellent for this club. They've got the club out of the doldrums."
Crewe: Turnbull, Otsemobor, Bougherra, Foster (Vaughan 62), Billy Jones, Bell, Grant, Lunt, Steve Jones, Taylor, Rodgers.
Subs Not Used: Tomlinson, McCready, Higdon, Johnson.
Goals: Billy Jones 4, Bougherra 17, Rodgers 24, Taylor 61.
Coventry: Fulop, Whing (Duffy 45), Shaw (Williams 26), Page, Hall, Scowcroft (Hughes 82), Doyle, Hutchison, McSheffrey, Adebola, John. Subs Not Used: Morrell, Thornton.
Goals: John 23.
Ref: M Atkinson (W Yorkshire).