The sides will meet again at Ewood Park on Wednesday evening to decide who will make the trip to Wembley for the semi-finals of the competition.
The Blackburn manager told reporters after the match: "I was delighted with the way the lads went about it. I had three or four players who were only 60 to 70% fit and we've got another chance to get through.
"It was difficult because the ball was changing hands that many times. I'd be surprised if there were three or four consecutive passes in the whole match.
"It's always going to be a battle when you come to The Den with the Millwall fans behind them. The game on Wednesday is going to be a completely different game."
The winner of Wednesday's replay will be the only side from outside the Premier League to make the final four.