The result has lifted Rovers out of the relegation zone for the first time this season, but Saunders, who took charge nine days ago, was quick to praise O'Driscoll's influence after the game.
"The previous manager did a brilliant job," said the former Wales striker. "He took the club forward and I imagine every fan will always be grateful for what he achieved.
"But sometimes in this game players can become complacent and the voice of the manager can go in one ear and out of the other.
"I've arrived with a different voice and given the lads the belief to go out and win games. Everything has started well and getting off the bottom of the table is a massive boost."
Doncaster next take on Leeds United in the Championship on Friday, October 14.