Their 4-1 thrashing of Coventry was only their sixth win of the season, but Sheffield Wednesday's shock win at Wolves means they are still 10 points adrift from safety at the bottom of the Championship.
After Billy Jones headed them in front as early as the fourth minute, Crewe were in the ascendancy.
Impressive Algerian defender Madjid Bougherra doubled the advantage with a header 12 minutes later and while Stern John reduced the arrears on 23minutes, Luke Rodgers conjured up a brilliant volley for the third a minute later, during an entertaining opening spell.
Rodgers was in inspired form for Crewe in the first half and could have added to his tally on more than one occasion. He lifted a close-range header over after Gareth Taylor had knocked the ball back for him and at the end of a blistering run saw his effort deflected the wrong side of the post by Robert Page.
Steve Foster came close twice to extending Crewe's lead, connecting a boot to a Kenny Lunt free-kick only to arrow his shot wide and then heading a corner from his skipper into Marton Fulop's arms.
Home captain Lunt was lethal with his deliveries from set plays and he set up Billy Jones' opener with a curling free-kick which the teenager headed in at the far post.
After Foster's header had been turned onto the bar by Fulop, Bougherra notched his first goal since arriving at Crewe on loan from French Second Division outfit FC Gueugnon by getting to the rebound first to head into the far corner.
And though John stabbed home inside the six-yard box after Dele Adebola had headed back James Scowcroft's deep cross, Crewe called all the shots.
Rodgers brought down a Lee Bell pass and volleyed in off the near post for his fifth of the season.
Then Steve Jones proved to be a real force in the second-half for the hosts, tormenting Coventry substitute Richard Duffy down the left flank.
The Northern Ireland international cut infield and dug out a shot into the keeper's clutches before Taylor unleashed a fierce 20-yarder which Fulop did well to tip over.
But Fulop was wrong-footed when Steve Jones' shot took a wicked deflection off Taylor and trickled in for the fourth on the hour mark.