The Black Cats ended a four-match losing streak with a hard-earned point at the Emirates Stadium.
Titus Bramble and his fellow defenders excelled as they limited Arsenal to few clear-cut chances. When the Gunners did carve out openings, goalkeeper Simon Mignolet was on hand to deny them.
"Our resilience was back, which was good to see," said Bruce. "We needed a big performance because we let ourselves down at Everton last week. I'm very pleased for the players.
"They got what they deserved. The last 10 or 15 minutes were a bit hairy but I thought we merited something from the game.
"We still had our moments and some of our football was good. We looked a threat on the break and everyone stuck at it.
"Hearts were in mouths in the last few minutes but we deserved something for our performance.
"We got a little bit of luck and a clean sheet. The result gets us off 37 points - we've been stuck there for ages."
very good
Mignolet saved superbly from Nicklas Bendtner in the first-half, while Arsenal substitute Marouane Chamakh hit the bar with a header late on.
Arsenal manager Arsene Wenger was pleased with the way his side continued to exert pressure as the match went on, but admitted that they lacked fluency.
"I'm very happy with the performance," he said. "I feel defensively we were very good, we gave a lot physically but we lacked a bit of creativity.
"What is frustrating [is] that we have given everything in the end but we lacked a little but of sharpness in the final third."
