The Tigers had goalkeeper Eldin Jakupovic to thank for keeping the hosts at bay as the Switzerland international made a number of important saves to keep the scoreline goalless.
With a Champions League tie against Barcelona on Tuesday night in mind, Arsene Wenger made nine alterations to his Arsenal side while Bruce went one further with 10 changes as he keeps his priorities purely on promotion back to the Barclays Premier League.
But the Sky Bet Championship leaders now face another fixture in an already packed schedule, with Arsenal also busy in the coming weeks.
Danny Welbeck, Theo Walcott and Joel Campbell were all kept out by Jakupovic as this repeat of the 2014 final - which Arsenal won 3-2 after falling two goals behind - ended in a stalemate.
The replay will take place at some point during the week commencing March 7 after the managers were at odds about keeping them in the build-up to this game.
Wenger said he was now “conservatively English” and felt replays should remain, while Bruce called for them to be axed and for ties to be decided on the day.
And, after Jakupovic’s heroics, the argument again came up as Bruce lamented the number of games his promotion-chasing side face in the run-in.
“I said before, there is nobody more traditionalist than me when it comes to the FA Cup but why can’t we just go to penalties?” he said.
“Why do we have to have a replay? Supporters have to find the money to support their team. In the past to win a European cup you had to play six or seven games, now it’s 17.
“We all love the FA Cup and for our club, the final was the biggest day in our lives. We play Ipswich on Tuesday and you know when you come to the Emirates you are going to have to run a million miles.
“A footballer can play three games in three days if he wants but you can’t play with the energy or intensity that you need to win a Championship game or an FA Cup tie.
“And that’s the big reason why. We have a game on Tuesday and then on Friday. Then the following Tuesday then Friday again. It’s ridiculous the number of games we have got coming up.”
Bruce was also full of praise for Jakupovic - who was making just his eighth appearance of the season - and defended his wholesale changes.
“He has waited long enough,” Bruce added.
“The form of Allan McGregor has been excellent too. I’m delighted for Eldin. It’s never easy to be a number two but he works hard every day and I’m sure he will remember that one. He made some good saves and kept us in the cup.
“The team I put out has over 600 Premier League appearances between them, so it’s not as though I am putting out a load of rookies.
“It’s a fine line between the so-called second team and the first team but that will do us a power of good and stand us in good stead.”
Arsene Wenger was left bemoaning Arsenal’s lack of cutting edge in front of goal as their fixture list continues to grow - and clarified his position on replays.
“The nightmare would have been to go out. The frustration is that we didn’t score and it’s not what we wanted, to have a replay, but between that and going out, we choose the replay,” he said.
“I am happy for the replay (as opposed to going out). We need to be more efficient in the final third, because today we had over 70 per cent possession and we will not have that on Tuesday night (against Barcelona).
“They defended well, because their ‘keeper played well, because our final ball was maybe not good enough.”
When asked about being in favour of replays, Wenger pointed to Britain’s current European Union discussions as a way to show the country likes to be different.
“I said I like the English formula because it’s a little bit special,” he added.
“I like the idea that in England you don’t do things like anywhere else. That’s why you negotiate in Brussels at the moment as well.”