U’s fail to take advantage of Crewe’s poor run of form at Gresty Road.
The Railwaymen had lost five of their previous six matches, taking just one point from a possible 18, but boosted their chances of avoiding the drop by overcoming a lacklustre U’s.
Shaun Miller grabbed the only goal of the game in the 61st minute.
Brandon Comley conceded a free-kick in a dangerous position, for a foul on substitute Tom Lowery just outside the penalty area.
Callum Ainley’s free-kick cannoned off the wall and Miller pounced on the rebound to tap home the ball from eight yards out.
The U’s remain three points adrift of the play-offs.