Kieran Sadlier bagged two before Ben Whiteman wrapped up the points as Rovers boosted their play-off hopes at London Road.
“I never get too high with the wins and too low with the losses,” he said. “One thing you will see from me is a consistency to try and keep people believing in what they are doing.”
Marcus Maddison was inches away from giving Rovers an early lead when shot just wide from 20 yards after three minutes.
But the visitors were ahead 14 minutes later after Sadlier opened the scoring with a low 30-yard strike against his former club.
Mo Eisa fired over following a deflection on 39 minutes, before Ivan Toney headed wide on the stroke of half-time as United enjoyed a good spell of pressure.
Tom Anderson headed a Toney effort off the line on 56 minutes to keep Rovers ahead.
Christy Pym pulled off a brilliant save at the expense of a corner to deny Niall Ennis five minutes later. But there was nothing he could do to stop Sadlier from turning home Jon Taylor’s resulting corner.
And Whiteman made the game safe with eight minutes to go following a superb counter attack.
After the game, Peterborough confirmed two arrests were made for alleged racist behaviour in the away end at the Weston Homes Stadium.
Both Sky Bet League One clubs issued statements on Thursday evening, saying they would work together in support of Cambridgeshire Police.
Doncaster said the club “abhor racism in any form”.
A Doncaster club statement read: “We take a zero tolerance approach to such issues and would expect to issue a substantial club ban to anyone proven to have acted in such a manner as well as require them to complete some educational actions before attending any Rovers games.”
Peterborough said in a statement: “The football club can confirm that there were two arrests made in the away section of the Weston Homes Stadium for alleged racist behaviour.
“The club and Doncaster Rovers are working together with the police on this matter.”
The Football Association has been contacted for comment.
Peterborough United: Pym, Mason, Bennett (Blake-Tracy 79), Kent, Ward (Boyd 62), Woodyard, Reed, Butler, Maddison, Eisa (Jade-Jones 63), Toney. Unused substitutes: O’Malley, Cartwright, Barker, Burrows.
Doncaster Rovers: Dieng, Halliday, Wright, Anderson, John, Whiteman, Sheaf (Coppinger 84), Taylor (James 72), Sadlier, Gomes, Ennis (Thomas 86). Unused substitutes: Lawlor, May, Greaves, Daniels.
Referee: D Rock (Hertfordshire).