The duo followed Walsall's Anthony Gerrard who received a straight red in the 63rd minute from a far from lenient referee Janil Singh.
Walsall, defending their 100% home record without conceding a goal, got away to a rip-roaring start and never looked back to chalk up their best home win of the season despite being reduced to ten men midway through the second half.
Daniel Fox and skipper Michael Dobson marked the occasion with their first goals for Walsall as the Saddlers completely dominated Peterborough with some fast, open attacking football to exploit some miserable defensive work by the Posh.
The win made amends for Walsall's defeat in their previous game at Grimsby and they could hardly believe how easy it was to overcome Peterborough, who had not previously conceded an away goal this season.
With Peterborough playing three at the back this created a lot of space for the Walsall attack and with skipper Michael Dobson surging forward the Saddlers were in control following an anxious opening ten minutes.
Both Lloyd Opara and the much travelled Trevor Benjamin could have scored for Peterborough in this spell and their failure proved to be expensive.
The pressure was relieved and Walsall exploited Peterborough's shortcomings when a square pass from Mark Wright to the unmarked Fox ended with a cracking left-footed shot past Mark Tyler.
To prove he could match the goal scoring exploits of Fox, Dobson stepped into the act in the 17th minute when Tyler pushed out Kris Taylor's cross and Walsall's skipper hammered home a powerful drive.
Ten minutes later Dobson popped up again to collect a pass pulled back by Martin Butler to score another gift goal.
Despite their plight Peterborough continued to attack and this allowed Walsall several more opportunities. Hector Sam, still seeking his first goal, failed with a poor header, while Taylor and Fox both had opportunities to increase their tally.
Branston found himself very much in the firing line and in the general confusion collected his fifth booking of the season.
But Gerrard got a harsh straight red card for a clash of heads with Benjamin and received a standing ovation as he left the field.
Despite being a man short Walsall added to their goals tally when Martin Butler headed home from close range following a left-wing cross from Taylor in the 74th minute.
Butler obtained Walsall's fifth five minutes later to highlight Peterborough's obvious problems.