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Doncaster's starting 11, out to impress O'Driscoll who replaced Dave Penney at the start of the week, began brightly with Sean McDaid having a shot blocked by David Worrell.
From the resulting corner Rovers captain Graeme Lee headed wide.
Lewis Guy then sprang down the left, cut inside Worrell and squared the ball across the area but the incoming James Coppinger could not control and skewed it wide.
Ritchie Partridge had a shot blocked by Lee after a break from midfield.
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Coppinger, playing behind the front two at the head of Doncaster's diamond midfield, flashed a volley wide from 20 yards as half-time approached.
The Rovers breakthrough almost came on 45 minutes when Gareth Roberts crossed to the back post for Adam Lockwood whose header bounced off the crossbar.
Rovers didn't have the same tempo as the first half and it was Rotherham who threatened at the start of the second with Partridge and Dave Hibbert both going close.
Neil Cutler then made a brilliant point-blank save from Lockwood who had been set up by Lewis Guy.
Lee then headed the corner across the face of goal and wide.
At the other end, Hibbert set up Will Hoskins whose flicked header bounded onto the roof of the net.
Lee Williamson spurned Rotherham's best chance 14 minutes from time.
The midfielder had earlier skied an effort from 20 yards but when the ball dropped after substitute Ryan Taylor had battled with Budtz for a deep cross, Williamson blasted into the side netting from 15 yards when it was easy to take a touch and side foot home.