Shaun Miller scored twice as Crewe beat Oxford to earn their first home win.
Danny Shelley set Miller up to lift the ball into the roof of the net and he added his second, side-footing home AJ Leitch-Smith's inch-perfect centre.
United had chances and Steve Phillips denied Alfie Potter, Asa Hall and Deane Smalley before Leitch-Smith took down Luke Murphy's ball and drilled home.
Liam Davis got Oxford on the scoresheet with a header from Josh Payne's cross and then hit the post from 30 yards.
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Crewe boss Dario Gradi told BBC Radio Stoke:
"I was surprised that we didn't go on to do better in the second half, because we were terrific first half.
"I said at half time that I thought they were all good, but the revelation is the front two - their combination play was too good for the opposition.
"We couldn't keep it going but, to be fair to Oxford, they put the pressure on us and had players all over the pitch that were good on the ball."
U's boss Chris Wilder told BBC Oxford:
"I never felt out of the game. When we made it 3-1, I thought we could get something out of it.
"It's important we don't go into our shell. It was a pretty spirited performance.
"Our general play, back to front, was excellent."