Substitute Greg Pearson's last-minute winner gave Crewe the victory and ended Oxford United's six-match unbeaten run.
Pearson was making his Alex debut after joining on loan from Burton and he tapped in from four yards after Nick Powell had taken on the home defence.
The U's had the best chances in the first half as Andrew Whing and Simon Heslop both shot over the crossbar and Peter Leven had an effort blocked.
Powell twice missed chances before he set up Pearson for the decisive goal.
VIEW FROM THE DRESSING ROOM
Crewe manager Steve Davis told BBC Radio Stoke:
"Only Cheltenham have come here and got a result so I think we've shown our credentials and what we're capable of.
"What you've got to think is that every time you come to these clubs, you've got to expect to win. That's what the top clubs do.
"We're not quite there yet because we're not one of the top clubs, but there's no reason why we can't be."
Oxford United manager Chris Wilder told BBC Radio Oxford:
"For 35 to 40 minutes we were exceptional. We knew it wasn't going to be easy and we started really strongly. But then we lost a little bit of belief because we had a lot of possession and a few chances but didn't get the goal.
"We played too slow in the second half. This is a big place for the opposition to come to and we are a scalp, we know that, we have to overcome that. We didn't play quickly enough in the second half, we didn't get the ball wide and the movement of the front three was almost non existent.
"The balloon was popped and we lacked belief and not for the first time we've got done with a late sucker punch. No-one has tracked the runner and a good ball has undone all the hard work of the past few weeks. The biggest disappointment is we lost heart and belief."