The Posh, who had averaged three goals per game in four straight wins, looked confident before the break and kept Rovers goalkeeper Ian Lawlor busy.
Doncaster enjoyed the lion's share of territory and possession after the break but lacked a bit of precision and finesse in the final third.
The stalemate leaves Rovers with six points from their opening five games and still searching for their first league win on home soil this season, following draws with Gillingham and Blackpool.
Tyler Garratt made his first league start for Rovers since August 16 last year as a replacement for Danny Andrew, while new loan signings Harry Toffolo and Jordan Houghton had to be content with a place on the bench.
Doncaster had a good opportunity to take the lead after 11 minutes - probably the best chance of the first half - when a mistake from Jack Baldwin was seized upon by John Marquis but his shot was comfortably saved by Jonathan Bond.
The hosts, matching up Peterborough's 3-5-2, had begun the game in solid fashion, while United looked sharp on the break. However, as a very watchable game progressed it the was confident visitors who gained more control and went closer to breaking the deadlock - keeping Lawlor on his toes in the Rovers goal.
Either side of the half hour the lively Marcus Maddison curled a superb effort off the bar and then saw another attempt from outside the area deflected just wide.
Lawlor palmed away a powerful shot from Gwion Edwards and also had to deny Jack Marriott as the home side were content to get in at the break goalless.
A nip and tuck opening to the second period saw Posh midfielder Michael Doughty shoot well over the bar from distance before Houghton, Liam Mandeville, and shortly after Andy Williams, were all introduced by Ferguson.
Rovers were now forcing the issue and Houghton saw a powerful shot blocked, Ben Whiteman struck a shot wide and Williams was denied a tap-in, following a surging run from Whiteman, only by a last-ditch block from Baldwin.
However, it was Peterborough that came closest to snatching all three points during the closing stages when an unmarked Steven Taylor headed straight at Lawlor from a corner.
Rovers: Lawlor, Wright, Butler, Garratt, Blair, Whiteman, Rowe, Mason (Houghton 60), Coppinger (Mandeville 60), May (Williams 71), Marquis. Subs not used: Marosi, Toffolo, Alcock, Ben Khemis.
Peterborough: Bond, Tafazolli, Baldwin, Taylor, Edwards, Lopes (Hughes 71), Doughty, Grant, Maddison, Morais (Kanu 61), Marriott. Subs not used: O'Malley, Shephard, Lloyd, Anderson, Forrester.
Referee: Graham Salisbury (Lancashire)
Attendance: 8,677 (1,696)