It was a feisty and frenetic first 10 minutes, with Crewe having the first chance after Joe Guest's speculative shot clipped the top of the bar.
But it was the hosts who took the lead after just three minutes. A corner from Alex Henshall was floated into the box and met with a solid rising header from defender Greg Leigh.
It was Henshall against who created another chance just moments later when the promising left winger's sizzling run was met by Jordy Hiwula, whose shot was blocked a Crewe defender with calls for hand-ball were dismissed by the referee.
The game was end-to-end and it was no surprise when Crewe fashioned an equaliser when Nick Powell's curling free kick was spilled by Angus Gunn, leaving Daniel Smith to slot home from close range.
Persistent gloomy drizzle created surface water on the pitch and the slippery conditions made life difficult for both sides, with many players frequently taking tumbles.
But it didn't seem to deter City too much and by 27 minutes the Blues had their lead back. Right-back Luke Coulson floated the ball into the penalty box and when Crewe's goalkeeper Ben Garratt misjudged the path of the ball, Hiwula pounced for his sixth goal of the season.
After half time City seemed to have more focus and determination and Crewe's Garratt was immediately forced into producing a fine save from Albert Rusnak.
The young goalkeeper was called upon by his team-mates several times during the second half, notably after shots by Hiwula and once again, the impressive Rusnak.
Towards the end Crewe pushed for the equaliser, leaving themselves vulnerable at the back. With the game stretched and only a few minutes to go, Devante Cole was brought down in the box by Alex defender Bernardo Pezo and 17 year-ago Rusnak stepped up- and tucked home the penalty with confidence to give City all three points.
Head of Academy Mark Allen admitted that the old adage of 'a game of two halves' was prevalent, with the Blues coming to life in the second half rather than being more focused in the opening 45.
"I think today wasn't one of our better performances," he said. "It was a lethargic first half performance if I'm honest. However I thought after half time we were much better during the second half and deserved the win.
"It's about the development of the players and making sure performances are over a 90 minute period. But still, a pleasing result nontheless and encouraging that the players responded well to their half time team talk."