Darren Ferguson’s team started the second leg how they ended the first, playing with a high speed and tempo, forcing the U’s deep into their own half.
After half an hour of relentless Peterborough pressure, Oxford were dealt a blow as midfielder Tyler Goodrham was unable to continue, Buckingham replacing him with ex-Arsenal academy player Marcus McGuane.
Posh levelled up the tie five minutes before the interval, Knight sneaking the ball into the net from the back post for his sixth league goal of the season after Burrows’ fine set-piece delivery from the left.
The U’s flipped the script before the break though, winning a free-kick just outside the area which Brannagan struck powerfully at the defensive wall, right into the arms of Burrows as he attempted to block the shot.
With the pressure on, Brannagan stepped up and calmly tucked the penalty into the bottom right-hand corner of Jed Steer’s net, restoring the Oxford advantage in the tie and shifting the momentum of the semi-final once more.
Peterborough’s tempo did not drop in the second half, Ricky-Jade Jones utilising his frightening pace to threaten down the left wing on numerous occasions and the home side piling the pressure on U’s keeper Cumming.
McGuane shot narrowly wide inside the final 10 minutes of regulation time, pulling a strike the wrong side of Steer’s post from a central position.
Posh relentlessly pushed in the final phases – and in the seven minutes of added time – with multiple shots but were unable to find the net.
Oxford and Bolton drew 0-0 when they met at the Toughsheet Stadium earlier this season but were then thumped 5-0 by the Trotters in March.