Posh, who had not won their opening four games of the season since 1961, made significant inroads toward breaking that 52-year record throughout the opening half, as goals from Tommy Rowe, Tyrone Barnett and Grant McCann helped their team to a healthy 3-0 advantage at the interval.
Lee Tomlin, whose goal was the difference against Oldham Athletic last week, came close to opening the scoring after spotting Rovers goalkeeper Owain Fon Williams off his line from 25 yards out, but his audacious attempt to lob the Welshman dropped narrowly wide.
Darren Ferguson watched on as his side took control of proceedings and monopolised possession, and it would not be long before the visitors saw their dominance pay dividends, with Rowe sweeping past Fon Williams after 14 minutes.
The hosts struggled to assert themselves on the game, and before long it was two. Michael Bostwick played in Barnett, who confidently found the right-hand corner of the goal.
The second half did not prove much better for the hosts, as club-record signing Assombalonga continued his fine scoring run by tapping home from close range, before Little's curling effort nestled in the bottom-left corner of the goal.