Posh managed a second equaliser through George Boyd just after half-time, but Rovers soon made the difference in numbers tell with Michel Salgado, Benni McCarthy and a Nicola Kalinic penalty completing a comprehensive 5-2 victory.
Sam Allardyce made seven changes to the side beaten 5-0 at Chelsea, with goalkeeper Jason Brown and midfielder David Hoilett elevated to the first XI as they had been for the previous rounds, along with teenage defender Phil Jones.
Salgado, Reid, McCarthy and Kalinic also came into the starting line-up, while there was a place on the bench for David Dunn, who had missed the weekend's game with a virus - thought to be part of the swine flu outbreak at the club.
Peterborough boss Darren Ferguson left striker Craig Mackail-Smith, who had a hamstring injury, out of his squad along with defender Gabriel Zakuani, with Krystian Pearce and Shaun Batt deputising.
Talk of swine flu in the Blackburn camp had dominated the build up to the match but the hosts looked anything but sluggish in the opening stages and went ahead after only three minutes.
Hoilett was brought down just outside the box and Pedersen calmly stepped up to rifle the free-kick over Lewis and into the roof of the net.
Peterborough were not disheartened though, and after Boyd had issued a warning with a dangerous free-kick that needed only a glancing header to finish, the visitors drew level with 17 minutes on the clock, Tommy Rowe crossing for Whelpdale to head back across the stranded Brown and in.
Blackburn almost found a response five minutes later as Hoilett connected with Pedersen's cross, but after the ball had bounced to him, Kalinic sent his header narrowly over the bar.
A scrappy period ensued and the visitors looked the more likely to add a second, with Whelpdale unlucky to steer a shot wide from Boyd's cross.
But Peterborough shot themselves in the foot three minutes before the break when Lewis brought down Pedersen in the area as the Norwegian midfielder raced onto a poor defensive header.
Lewis was shown a red card and Reid put the resulting penalty past substitute keeper James McKeown to restore Rovers' lead going into the break.
It seemed a straightforward task for Blackburn from there, yet within five minutes of the restart Peterborough had levelled again.
Whelpdale was involved once more, surging forward and squaring the ball to Boyd, who had the time and space to lash a ferocious strike past Brown with his left foot.
Blackburn then wasted a glorious opportunity to regain the lead as Hoilett fed a tricky ball across the box, Emerton failed to make contact and then Pedersen blazed his shot over the bar when it seemed easier to hit the back of the net.
The Premier League side soon made amends though as Salgado struck his first goal for the club, the Spaniard getting on the end of a delightfully lofted pass from Emerton in the 57th minute and slipping it in at the near post.
The man advantage was starting to tell and Blackburn scored their fourth with just under 20 minutes remaining when Kalinic capitalised on an error to play in McCarthy for an easy finish.
Kalinic then added a fifth two minutes later, converting confidently from the spot after Martin Olsson's cross was handled.