A cagey first half saw both sides struggle to create meaningful chances, but that changed after the break.
After the home side had hit the woodwork three minutes after half time, goals from Freddie Sears, Rhys Healey and Sanchez Watt in the space of eleven minutes gained the U's the points.
The win - and a fourth clean sheet in five - took the U's out of the bottom four, ahead of the long trip next weekend to Preston North End.
The U’s began the game with a fortunate free kick, as Sanchez Watt looked to lose his footing rather than being fouled on the edge of the box.
George Moncur stepped up to whip his right foot effort goalwards but Garrett in the home goal saw it all the way and tipped it over his crossbar.
For the next few minutes, Crewe had the better of the possession but were not getting in behind the U’s defence and Sam Walker wasn’t troubled.
The hosts had their first sight of goal with fifteen minutes gone, but Walker still wasn’t called into action as Waters’ effort went safely over the bar.
Both teams were trying to get the ball down and play and chances were exchanged around the twenty minute mark, as Tom Eastman headed straight at the keeper and Grant shot over from an acute angle.
Two crosses, from Moncur and Sean Clohessy, were put into dangerous areas behind the home defence but on both occasions, the ball went safe without a U’s player being able to get on the end of it.
Freddie Sears managed to find a yard for himself in the penalty area but as he turned, his effort was blocked before it could test Garrett.
The final chance of the half came on thirty eight minutes, with Ben Gordon keeping the scores goalless thanks to a goalline clearance.
Waters had cleverly got in behind but Walker stood up long enough to force him wide before he turned and shot goalwards, with Gordon getting back on the line in time to clear.
The U’s had conceded very few opportunities for the hosts so Humes would have been relatively pleased with his defence, but would have wanted more going forwards.
Both managers would have wanted a better tempo from their respective teams and it was the hosts who had the early chances in the second half.
Within a minute, Leigh got to the ball before Ben Gordon but couldn't keep his shot low enough to test Walker.
He went close sixty seconds later though, as his header rebounded off the post and safely into the U's stopper's hands.
Walker then comfortably held a volley from Grant, as the home side looked for the goal that could help them off the bottom of the league.
With the U's under a bit of pressure, boss Tony Humes made a brave substitution, bringing on striker Rhys Healey for midfielder Craig Eastmond.
It was the Cardiff City loanee's U's debut and the change bought about a change in the game, with the U's scoring three goals in eleven minutes.
The first came on fifty six minutes, with Freddie Sears making it five in ten games this season.
Sanchez Watt ran at Tootle down the U's left and having beaten the right back down the outside, drilled a ball across the box.
Loanee Alan Tate couldn't intercept and after taking an assured touch to steady himself, Sears shot to Garrett's left for the U's opener.
Six minutes later, Gavin Massey, now playing behind Sears and Healey, slotted a perfect through ball to the U's debutant, who calmly finished past the keeper to open his U's account.
It got even better for the visitors on sixty seven minutes, as Watt reacted first to make it three.
Healey found strike partner Sears on the right and after moving the ball away from his opponent, Sears hit a low cross into the six yard box.
Tate got to it first but Garrett had to save smartly to prevent an own goal - but was helpless as the ball ran out to Watt who made it 3-0.
Drey Wright replaced Sears but the change didn't upset the U's and it was they who looked the most likely to add to the scoreline.
Watt wanted another but was thwarted by a deflection when he found space to shoot from the edge of the box.
Former Crewe graduate David Wright came on for the U's to great applause from the home crowd, those that remained, but didn't see too much action before the referee blew for full time.
It was a great second half performance from Humes' squad, and the fourth clean sheet in five games in charge made it a good day's work before the long trip back to north Essex.