Goals from skipper Luke Murphy, from the penalty spot, and Mathias Pogba in each half, either side of George Porter's equaliser for the U's, secured the Railwaymen victory.
Crewe's win helped them reach the 50-point mark in npower League One and after two successive defeats, boss Davis admitted it was a relief to get three points.
Davis said: "I'm delighted with the result. It was a hard-working, battling performance and it's got us the three points.
"Over the last couple of games we've struggled to find form and we need to get the results to get us over the line.
"We wanted to get to the 50-point mark that we set at the start of the season just to get us over that line.
"It was a bit of a relief to get the win, in a game of few chances. It was a little bit of a battle and we knew that we had to come here and work hard and fight for everything and the lads did that.
"In the first half I thought that we dictated the play and dominated the game, in terms of our football.
"It forced them to change their shape to a 4-4-2 from 4-3-3 and they had a good spell just up to half-time.
"We got them in at half-time and sorted one or two things out and in the second half, it became a little bit scrappy. There weren't too many chances, but we managed to convert our's."