Luke Moore's brace put the visitors in charge and they were cruising when Chris Brunt made it 3-0 in the 41st minute.
But Peterborough rallied with Craig Mackail-Smith's diving header on the stroke of half-time giving them hope.
Aaron McLean pulled another one back for Posh in the 53rd minute but Albion closed out the game, despite Graham Dorrans' 90th-minute dismissal, to make it seven points from their opening three games.
Greening omittedThe news that West Brom captain Jonathan Greening was left out of their squad raised serious questions over the midfielder's future after he handed in a transfer request earlier this summer.
Greening's shock absence could have had an adverse effect on the Baggies but the visitors flew out of the blocks and made the breakthrough after just three minutes.
Gabriel Zakuani surrendered possession to Moore on the edge of the box and he fired a speculative effort towards goal that Posh keeper Joe Lewis allowed to squirm under his body and into the net.
Albion continued to dominate the early stages and Posh boss Darren Ferguson was forced to adopt a more attacking intent with only 15 minutes on the clock in an attempt to change matters.
Ferguson soon saw his charges grab a foothold in the game, with Albion keeper Scott Carson called upon to make a great save from McLean, and Mackail-Smith somehow put wide from close range.
But West Brom capitalised and Moore doubled their lead in the 34th minute, converting from 12 yards after a neat through-ball from youngster Chris Wood.
Brunt then converted after good work from on-loan debutant Shaun Cummings down the right, but there was still time for Mackail-Smith to head home from Shaun Batt's cross.
FightbackPeterborough really looked to impose themselves at the start of the second half and soon got their reward.
The impressive George Boyd put a cross into the box from the left-hand side and McLean beat Jonas Olsson to poke home from six yards.
A thrilling encounter looked to take a new twist shortly after as the hosts had the ball in the net once again but, with London Road celebrating, referee Graham Horwood rightly ruled it out for a foul on Carson.
Lewis made a smart stop from Moore at the other end just after the hour mark as Albion came back forward.
But they did enough in the remaining quarter to hold on for a hard-fought victory, with Dorrans' dismissal for a bad foul on Charlie Lee a disappointing way to finish.