John Oster was then sent off for an off-the-ball offence on Grant McCann and Cliff Byrne headed Scunthorpe back into the game.
Quinton Fortune saw red for a tackle on Byrne and in the second minute of six added on, Woods handled in the box and McCann struck home the penalty to earn a point.
And although O'Driscoll was disappointed to miss out on a win, he could not criticise referee Keith Stroud for any of the decisions.
O'Driscoll said: "Up until John Oster's sending off we were in total control. John knows better, he claims he got punched by someone else and reacted but you can't react, he knows that, so no complaints.
"No complaints about Quinton's tackle and no complaints about the handball.
Rovers were by far the better side until the first sending off and O'Driscoll will not allow the frantic final 15 minutes to take the shine off what had been a fine performance.
He continued: "Last week (against Ipswich) I was really disappointed with some aspects of our play but today we were excellent and I am not going to let the last 15 minutes taint it.
"On the last 15 minutes a draw was the fair result but I'm disappointed because we thought we were going to win by three or four and in the end we were hanging on."
Scunthorpe manager Nigel Adkins was delighted with his side's comeback, which stretched their unbeaten league run to four games.
"They did a great job on us. They were on top in the first half," he said.
"It was great character shown to come from two goals down to go and get something out of the game, good discipline to keep 11 players on the pitch and great entertainment for the supporters.
"First half to Doncaster, second to Scunthorpe."
The fourth round draw for the Carling Cup was made while Scunthorpe were in action and they were drawn against Manchester City, a tie which Adkins is looking forward to.
He said: "What a fantastic tie that is for us.
"We will go to a magnificent stadium and play against a team who are going to put all their top players out, they are expected to beat us but anything can happen in football.
"It's a big tie that we wanted. Hopefully we can make a few bob out of the competition, we go there without any pressure on and hopefully we can go and enjoy it."