Darren Ferguson's men created several chances, particularly in the second half, but couldn't force a winner as the game finished goalless.
An error from Ricardo Santos allowed Theo Robinson the first effort on goal at the ABAX Stadium, but the striker's effort from long range was routine for Ben Alnwick.
Marcus Maddison fired over from a well-worked Posh free-kick on 20 minutes, Oztumer sliding it low for the former Gateshead man, but he couldn't get his head over the ball and didn't trouble Sam Johnstone in the Doncaster goal.
An optimistic effort from Maddison flew well wide of the target on the half hour mark after Oztumer had showed determination to ride a few challenges in midfield.
Furman curled a shot into the side-netting on the stroke of half-time for the visitors. At the break, Posh made a change with Michael Smith replacing Ricardo Santos.
Bostwick was cautioned for a foul by the touchline by referee Mr Sutton on 48 minutes. Stevens was denied by a fine stop from Alnwick before Luke James' went on a lung-bursting run which ended with a deflected effort that whistled just past the far upright.
Forrester smacked a superb free-kick against the crossbar on 54 minutes as Payne was penalised for obstruction 30-yards from goal.
James was superbly denied from a tight angle by Johnstone as Posh continued to make all the running.
Furman planted a header wide of the target on 70 minutes before Posh made a double change. Mendez-Laing saw a powerful drive beaten away by Johnstone before Payne scooped over from close-range.
Final Score: Posh 0-0 Doncaster Rovers
Posh: Alnwick, Santos (sub Smith 46min), Burgess, Bostwick, Newell, Payne, Oztumer, Maddison (sub Mendez-Laing 76min), Beautyman, James, Mclean (sub Washington 77min). Unused subs: Day, Vassell, Anderson, H. Anderson.
Doncaster: Johnstone, Furman, Robinson (sub Main 82min), Forrester (sub Whitehouse 90min), McCullough, Butler, Stevens, Keegan, De Val (sub Middleton 33min), Wabara, Coppinger. Unused subs: Marosi, McCombe, Wakefield, McKay.
Attendance: 6,895 (898 Doncaster fans)