Against one of the promotion favourites Stuart McCall's men had to dig deep to secure back-to-back wins, but Bower's well-placed header was just reward for a spirited second-half display.
Posh boss Darren Ferguson will be disappointed that his talented side failed to make more of their first-half dominance, but in truth it was deep into injury time before Bantams keeper Donovan Ricketts was forced to make a real save.
United bossed large parts of the opening period, but with City's back four holding firm they struggled to carve out clear-cut chances.
Impressive full-back Claude Gnapka threatened with his surging runs and clever striker Danny Crow tried his best to find the breakthrough, but too often United's attacks produced no end product.
The visitors should have done better after 25 minutes when Crow burst clear after a lucky rebound, but when he picked out hot-shot Aaron McLean with an excellent pass the Posh striker dragged his drive wide of the mark.
Gnapka was booked after a reckless lunge on Eddie Johnson and the Frenchman was fortunate to stay on the pitch when he later upended City winger Omar Daley.
McCall must have been relieved to have gone in at the break with his side still level and they came out with more urgency in front of another home crowd of over 13,000.
The decisive moment came after 56 minutes when Posh defender Craig Morgan was penalised for pushing Peter Thorne and the United defence failed to stop Bower getting his head to Paul Heckingbottom's chipped free-kick.
A minute later Heckingbottom got in a vital tackle on Josh Low as he threatened to bear down on the City goal.
Thorne almost grabbed a second for City during a frantic goalmouth scramble, but Posh staged a late rally and almost salvaged a point.
McLean put a header over the bar, and Morgan scooped a difficult chance over the bar with three minutes to go.
As City hung on tricky winger Jamie Day came closest to snatching a draw, but his angled drive was brilliantly tipped over the bar by Ricketts.