Elliott Moore’s second-half header put Des Buckingham’s side in front, and the U’s held on despite increasing pressure from the visitors towards the end.
The winners of the game will face either Bolton Wanderers or Barnsley at Wembley on May 18.
Oxford had beaten Peterborough 5-0 in their last encounter but this proved a completely different type of game, with nerves evident on both sides.
The decisive moment at Grenoble Road came when Cameron Branagan headed Josh Murphy’s corner back at the far post, with Moore supplying a finishing touch.
Ricky Jade-Jones had the best chance to level the scores, prodding Kwame Poku’s cross wastefully wide midway through the second half.
Oxford head coach Buckingham said: United head coach Buckingham said: “It’s an advantage, but we’re only halfway through. I’m happy with what I’ve seen tonight.
“In the first half, I thought we were very good, and in the second half, there were a few things we need to tidy up on going to their place on Wednesday.
“To come away with an advantage was important because they’re a very good team. We saw that when we played them at their place, and the last two occasions when we played them. I’m sure Wednesday will be a very tough challenge for us.
“If we can take the energy levels and the understanding of what we’re trying to do, the way I’ve just seen tonight, then I’ll be very happy.”
Peterborough boss Darren Ferguson said: “The tie was never going to be settled in one game. Oxford will start as favourites next week because they will start the game in front. That’s the position I would rather be in, but we have been good at home, the atmosphere will be great and hopefully we will get the job done.
“We wanted to take no risks in the opening 10 minute or so because we knew they would fly at us which is why we were hitting the ball longer than normal, but we then didn’t help ourselves by continuing to hit the ball too long too early. We weathered the frenetic start, but right up until they scored we weren’t good enough in possession. We were solid out of possession, but with the ball we didn’t play like we can.”
Oxford United (4-3-3): Cumming; Stevens, Moore, Brown, Bennett; Rodrigues (McEachran 71), Brannagan, Goodrham (Bodin 77); Dale (Browne 71), Harris, Murphy.
Not used: Eastwood, Long, Leigh, McGuane.
Peterborough United (4-2-3-1): Steer; Katongo, Knight, Edwards, Burrows; Kyprianou, Collins; Ajiboye (Poku 46), Randall, Mason-Clark; Mothersille (Jones 59).
Not used: Bilokapic, de Havilland, Clarke-Harris, Fernandez, Dornelly.
Referee: Lewis Smith (Lancashire) Attendance: 11,125