Moore nodded home nine minutes into the second half, with the U’s then holding on to their lead despite increasing possession and pressure from the away side.
Des Buckingham named an unchanged line-up from the side which won 2-1 at Exeter City last weekend, to seal a place in the top six.
The only alteration to the squad was the return of Sam Long after illness, as he replaced James Henry on the bench.
United made a fast start to the game, and penned the visitors back, but were unable to make it count in front of goal.
Ruben Rodrigues sent an early volley from the centre of the penalty box down the throat of Posh goalkeeper Jed Steer, while at the other end, Joel Randall slid Ephron Mason-Clark in down the left, but Jamie Cumming was able to deal with the low strike.
Midway through the first half, Tyler Goodrham let fly from distance, and his volley was only narrowly off target.
After the torrid time Josh Murphy gave Jadel Katongo in the league fixture just three weeks prior, the U’s winger was well marshalled in the first half an hour.
Murphy though grew into the tie, and found a route towards goal when he held off Katongo and cut inside from the byline, only for his shot aimed at the near post to lack any conviction.
Minutes later, Murphy got down the left and sent in a cross-cum-shot which skimmed over Steer’s crossbar.
The biggest chance of the half fell six minutes before the interval, when Joe Bennett whipped in an inswinging corner which Moore headed over from inside the six-yard box.
Kwame Poku came on at half-time in place of David Ajiboye for the visitors, and had the first chance of the second period, when he came inside onto his left foot and fired narrowly over from 18 yards.
Nine minutes into the second half, the U’s took the lead when a deep corner from Murphy was headed across goal at the back post from Brannagan, with Moore able to nod home from close range.
A nervy spell in the game followed, and it was only natural, as United were caught in two minds as whether to push on, or sit tight, while the visitors struggled to break the U’s down.
With 68 minutes on the clock, Hector Kyprianou found space 25 yards out and powered a shot into the midriff of Cumming.
Buckingham then made his first alterations three minutes later, when Josh McEachran and Marcus Browne replaced Rodrigues and Owen Dale respectively, while Billy Bodin came on for Goodrham not long after.
The Posh continued to press for an equaliser, with a backheeled effort from substitute Ricky-Jade Jones well held by Cumming, while Ronnie Edwards headed over from a Harrison Burrows corner, when he probably should’ve hit the target.
Cumming then pawed away a shot at his near post from Burrows, while Jones got his feet mixed up and prodded wide from a Poku cross.
The nervous tension grew as each minute ticked by, but after three minutes of stoppage time were added on, the noise again grew inside Grenoble Road as United saw out the game to earn the advantage going into Wednesday night’s second leg.
Oxford United (4-3-3): Cumming; Stevens, Moore, Brown, Bennett; Rodrigues (McEachran 71), Brannagan, Goodrham (Bodin 77); Dale (Browne 71), Harris, Murphy.
Unused subs: Eastwood, Long, Leigh, McGuane.
Booked: Rodrigues, Bennett.
Peterborough United (4-2-3-1): Steer; Katongo, Knight, Edwards, Burrows; Kyprianou, Collins; Ajiboye (Poku 46), Randall, Mason-Clark; Mothersille (Jones 59).
Unused subs: Bilokapic, de Havilland, Clarke-Harris, Fernandez, Dornelly.
Booked: Mason-Clark.
Referee: Lewis Smith (Lancashire)
Attendance: 11,125 (TBC visitors).