The hosts, who made seven changes from the side that lost at Charlton on Saturday, were forced into a further early change when Matt Bloomfield suffered a broken nose in a challenge with Tommy Rowe.
But Wycombe still made a positive start, and Jon-Paul Pittman wasted a great chance to put them ahead when he drilled wide from close range early on.
It did not take too long for Darren Ferguson's men to get into their stride though and they silenced the home support with two goals within the space of ten minutes midway through the half.
Firstly Aaron McLean was given the time and space to sweep home Boyd's corner when just yards out.
And minutes later, further defensive hesitancy allowed Rowe to steal in and poke Tom Williams' cross past the floundering Jamie Young.
The visitors started to ooze class and Wanderers were left chasing shadows for much of the half, although Stuart Beavon and Matt Phillips did have shots blocked in a rare Wycombe rally.
Things were no different after the interval as the hosts struggled to gain any foothold on the game as Peterborough kept up the pressure.
It was Boyd who provided the highlight of the night, shuffling his feet before firing a swerving 30-yard drive into the roof of the net to kill the game as a contest.
And on 68 minutes United further stretched away, Shaun Batt setting up Lee Frecklington to smash home past a helpless Young.
The game dwindled to a close with a flurry of substitutions.