The Bees started brightly with Jason Norville looking lively up front.
However, the visitors then started to enjoy the better of the play and from a good move down the left flank, Danny Crow's neat flick set-up Calum Willock, though his low effort was well saved by home keeper Ross Flitney.
The Posh grew in confidence and it was no real surprise when they took the lead in the 13th minute.
Crow began the move, setting Ryan Semple down the right and when his cross wasn't dealt with by the home defence, Crow was on hand to provide an easy finish from a couple of yards out.
He should have claimed his second with ten minutes of the half remaining, but he horribly miscued his shot from Jamie Day's cross.
The visitors paid for that miss minutes later when Paulo Vernazza set-up Yakubu, who fired into an unguarded net for his first goal of the season.
With the famous Underhill slope in their favour in the second half, the home side began to enjoy the better of the play.
Lee twice tested Mark Tyler in the Posh goal, first from a 20-yard free-kick and then heading Vernazza's delivery straight at the keeper.
However, it was to be third time lucky for the midfielder when a short corner caught the visiting defence napping, and from captain Ian Hendon's inch-perfect cross, Lee was left unmarked, six yards out to head home.
Peterborough had chances to rescue a point, notably through substitute Adam Newton, who wasted a glorious last-minute opportunity that saw him somehow blaze over with the goal at his mercy.