Dan Jarvis gave Sports the lead in the 29th minute, eight minutes after Aidan Elliot-Wheeler saw red.
Peterborough Sports doubled their lead just after the interval, with Mark Jones turning home from close range.
Sports wrapped up the points in the sixth minute of added time, through Rory McAuley.
Banbury gave three new players their debut for this game, and from the opening whistle, United were on top of their game.
In an end-to-end start, Jack Harding made a good save in the sixth minute, and new signing Joshua Johnson went close with a glancing header, sixty seconds later when Aidan Elliott-Wheeler put him through.
In the 17th minute, Elliott-Wheeler went close, with visiting ‘keeper Peter Crook saving well after another new signing, Lewis Darlington, had put the ball through to him. Three minutes later, Tai Fleming did well to block an effort from the Turbines as the play swung from one end to the other.
The game changed in an instant in the 22nd minute when Elliott-Wheeler made a late tackle in a ‘last man’ situation and was promptly shown the red card for the denial of a goal-scoring chance, reducing Banbury to ten men.
The visitors almost immediately took complete control of the game as Banbury found it difficult to cope with one player missing. After failing to put away a couple of chances in the 25th and 27th minute, Peterborough took the lead in the 29th minute when Dan Jarvis rifled in a 20 yard left-foot shot, to give Harding no chance.
United were suddenly under severe pressure, and Sports spurned four good chances in the final ten minutes before the break, the second one of the four was well-saved by Harding as he tipped the ball round the post for a corner.
Two minutes into the second-half, the Turbines doubled their lead when Mark Jones did exceptionally well to convert a rocket-fuelled cross at the near post, before anyone had a chance to intercept.
Four minutes later, Ken Charles went close with a chance, before Harding again showed why he is so prized by Banbury after saves in the 70th, 71st and 75th minutes.
Craig Hewitt was introduced off the bench in the 74th minute, and suddenly United looked as though they might just get back into the game as Hewitt caused all sorts of problems for Sports’ right back, and the visitors certainly had a problem with his pace that they had to work hard to counter.
Rory McAuley managed a third goal for Peterborough in the fifth minute of time-added-on which Banbury hardly deserved, but the whole reason for the defeat was playing the vast portion of the game with 10 men.
Banbury United: Jack Harding, Simeon Maye (captain), Luca Woodhouse (80 mins. Zach Scott), Tai Fleming, Aidan Elliott-Wheeler, Ken Charles, Lewis Darlington (74 mins. Craig Hewitt), Harley Giles, Joshua Johnson, Louis Hall (80 mins. Jack Davies), Emmanuel Maja. Subs: (not used) Albert Wood, Ricky Johnson.
Peterborough Sports: Peter Crook, Joshua McCammon, Elicha Ahui, Dan Lawlor, Dan Jarvis, Mark Jones, Ryan Fryatt, Rory McAuley, Ashton Fox, Gabe Overton, Hugh Alban-Jones. Subs: Kaine Felix, Ben Fowkes, Connor Johnson, Matthew Miles, Sidney Pereira.
Attendance – 452
Thank you to Barry Worsley for the match report.