A Charlie Lee thunderbolt and an Aaron McLean strike sealed the win as both Lee McEvilly and Graham Branch were given their marching orders for Stanley.
Peterborough had the better of the opening stages, with Jamie Day in particularly impressive form in midfield.
He continually cut in from the left flank to trouble the Stanley defence and it was his vision that created a golden opportunity early on.
Day clipped a ball over the top of the Stanley defence and when McLean was brought down inside the area by Graham Branch, the referee didn't hesitate in pointing to the spot.
But when McLean took the penalty himself, Kenny Arthur got down well to his right to make the save.
Despite that setback, however, the visitors continued to threaten.
Arthur was forced into action again to save George Boyd's attempted lob, while Day twice flashed efforts just wide of the post.
Meanwhile, Accrington's only real chance of note came when Romuald Boco fizzed in a shot from an almost impossible angle that skimmed Peterborough's bar.
But, as the half came to a close, both teams burst into action.
First the visitors had a goal chalked off when Day converted Morgan's flick on from an offside position.
Then, Stanley skipper Paul Mullin headed over from eight yards after he had been picked out by Boco.
The high tempo continued after the break but once again Peterborough were in command.
And after Arthur had made another good save to deny McLean from close range, they surged in front on 55 minutes.
Day was again involved, taking a free kick quickly from the left to give Lee the time and space to blast an absolute rockett past the despairing Stanley keeper.
Things went from bad to worse for Stanley as substitute McEvilly was sent off 10 minutes after coming on for a stamp on Day and Branch followed for a second yellow card.
Then McLean wrapped things up with a good strike in injury time.