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.
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.