Morgan was the first to go for the hosts but Derby failed to take advantage until Bennett brought down Campbell in the penalty area in first-half injury time.
The defender was dismissed and Steve Davies held his nerve from the penalty spot.
Minutes after the break Campbell, a constant menace to the home side, added the crucial second.
And with 25 minutes remaining Campbell, on loan from Leicester, leaped to meet Kris Commons' cross with a conclusive header.
Peterborough manager Mark Cooper gave debuts to Reuben Reid, Izale Mcleod and Jake Livermore as the Posh looked to grab their second win in 13 matches.
McLeod almost made an immediate impact for his new side.
In the fourth minute the striker, on loan from Charlton, picked up the ball 18 yards out and unleashed a right-footed shot, but it went wide of the post.
The early warning shot roused Derby into action.
Twice in three minutes Davies was guilty of heading wide from inviting crosses by Nicky Hunt and Campbell.
And when Davies did locate the target with a header from Paul Green's cross, Peterborough goalkeeper Joe Lewis pulled off a good save with his feet.
But Peterborough were forced further on the defensive in the 28th minute when Morgan was dismissed for serious foul play.
Morgan was shown a straight red card for a late tackle on Campbell near the touch line. The referee had no hesitation with his decision.
It meant an early end to McLeod's debut as he was sacrificed for Charlie Lee barely half an hour into the game.
Reid, now leading the line for the hosts, threatened to give Peterborough the lead.
But his right-foot shot from Scott Griffiths' cross was saved by Stephen Bywater.
With three minutes to go before the break Campbell fired a right-footed shot from 12 yards but it failed to beat Lewis.
After negotiating 20 minutes a man down, the hosts looked as though they would survive until the break.
But in injury time, things got worse.
Again the tricky Campbell caused problems and this time drew a challenge from Bennett as he advanced into the penalty area.
The red card followed and the Posh were reduced to nine men.
Davies assumed the responsibility and dispatched the spot-kick into the bottom left corner.
Derby doubled their lead minutes after the restart.
Campbell followed up an initial effort that was parried by Lewis with a calm finish from 12 yards out.
Lewis prevented Peterborough from going further behind in the 59th minute as he fielded Shaun Baker's header with minimal fuss.
But he could do nothing to prevent Campbell heading Derby's third from close range with 25 minutes remaining.