League One Orient were only a minute from causing an upset in East Yorkshire 10 days ago and rattled the Premier League hopefuls with a freak late equaliser from Dean Cox to take the replay to extra-time.
But Tom Cairney struck with three minutes remaining to secure a 2-1 win and an all-Yorkshire tie with Barnsley in round four.
"All credit to Orient, they have given us two really difficult games and if we're honest we could be out of the cup. But we're not," said Bruce.
"We had some good chances to put the game to bed but when it's just 1-0 you are always on edge and they've scored with the last kick, really, to take it to extra-time. Then it's anybody's game.
"You hope a little bit of quality comes through in the end but fair play to Orient, they took us to two really hard cup ties and on another day could have gone through."