A game of massive commitment and polish saw City secure their second place in League One while Crewe had to come to terms with a red card for their playmaker Gary Roberts.
He was sent off in the second half for retaliating to a two-footed challenge from home skipper Louis Carey.
It looked a controversial ruling as both players could have gone but referee Paul Crossley, right on top of the incident, decided the City man was the victim of violent conduct.
City will be without defender Jamie McAllister for their top of the table clash with Nottingham Forest next Saturday after he picked up his fifth card for a trivial offence near the end while Crewe fear they may have lost Michael O'Connor to a long-term ligament injury after he was stretchered off.
In a generous tribute, the City programme described Crewe as "arguably the most attractive side in the country", a tribute based on their role as the League's top scorers.
City manager Gary Johnson sent his team out to shatter that image in the flat-out bid to snatch the vital first goal.
City laid down their markers with Scott Murray a lively raider on the right before he switched inside for a calculated shot turned away late for a corner.
Lee Johnson was providing the service from the home midfield so often testing his rivals as they gave him too much room.
When Crewe managed to break out Nicky Maynard underlined their scoring threat, first with a 20-yard shot which bounced off Carey for a corner and then one which was arrowing towards the bottom left-hand corner before a diving Adriano Basso saved it.
Then, inside seven minutes, City grabbed the game by the scruff of the neck and gave it a good shaking.
On 26 minutes McAllister, who had always been surging forward from left-back, broke away from the halfway line to cross for Murray to get in a glancing header which brought him his first goal since the second game of the season.
Crewe's suspect defensive qualities were then quickly tested again by the lively youngster Jennison Myrie-Williams who threaded a way to the byline before turning the ball back for a predatory Scott Brown to deliver the second goal.
The Railwaymen claimed a goal back after Carey brought Maynard down. The kick was a long way out but Basso fumbled and Luke Varney poked the loose ball back past him for his sixth goal this season.