Faris Haroun struck twice to put Boro on the way to a seemingly routine win, but Posh's loan star Dwight Gayle mirrored the Belgians trick to and drew the hosts level early in the second half.
Both sides had chances thereafter, and Mowbray was grateful that his side converted one when substitute Ishmael Miller bagged the spoils 14 minutes from time.
Mowbray said afterwards: "We came here to win, we would have been disappointed to draw and yet we could even have lost.
"It was all about the three points and we got them in the end.
"We set up to play on the counter-attack and after 25 minutes it looked like the right tactic but we didn't go on to dominate the game in the way we should.
"A fantastic goal brought Peterborough back into it and a sloppy one got them level, but I'm thankful our changes worked well.
"Ishmael was a real thorn in Peterborough's side. He was unlucky not to play from the start but showed his hunger to help the team by coming on and doing the business.
"The fact that Peterborough are bottom shows just how strong the Championship is as a league."