Mikael Mandron's first-half double put the League One side on the path to victory in their first win in all competitions since they defeated Wigan Athletic in the same tournament in October.
Teenager Joe Robbins made sure of the victory late in the game with a goal on his professional debut in a brilliant outing for the home side that saw them end the group stage boasting a 100% record.
Story of the match
James Collins added experienced goalkeeper John Ruddy to his squad for their final fixture in the tournament whilst also starting Oskar Ruur at centre-back.
Defender Terrell Thomas was the only remaining Crewe player in the starting line-up that lost 3-0 to Swindon Town over the weekend.
Currently sat rock bottom of League One, Crewe dominated throughout the 90 minutes and could have four goals up by the break with their deadly attackers J'Neil Bennett and Mandron impressing.
Bennett struck Ruddy's crossbar with a looping header and directed efforts at the goalkeeper on another two separate occasions. The Tottenham Hotspur loanee caused the Wanderers defence all evening.
David Artell's side took the lead when Mandron brought the ball down with his chest, turned with ease and slotted the ball into the bottom corner following Oli Finney's decent cross.
Wolves had a big chance to equalise through Harry Birthwistle, but the defender's back-post attempt was right at Will Jaaskelainen.
Josh Lundstram, who was playing at right wing-back despite being a midfielder, almost made it two when the ball fell to him in the box, but his powerful effort cannoned off the post.
Alexandra doubled their lead when Mandron pounced on his initial attempt, which struck the post, to tuck the ball away to net his fifth goal of the season.
Into the second half and the visitors had a more cutting edge about them. Chem Campbell's good footwork and trickery nearly saw him cut the deficit, but he was denied by a Crewe block.
He drove into the box before drilling the ball into Ruddy's grasp with ease.
Chris Long thought he has scored a third in the final 15 minutes of the game after he latched onto Callum McFadzean's cross perfectly, but the offside flag went straight up.
Crewe did grab a third with just over 10 minutes when Robbin's deflected strike topped off a perfect professional debut for the academy player.
Next up for Collins' side is the trip to local rivals Birmingham City on Friday night before a 10-day break.
For Crewe, they also travel to a local rival in Bolton Wanderers on Friday, with the game on Sky Sports.