Nicklas Bendtner opened the scoring in just the second minute to set the tone for an effervescent outing from the Premier League table toppers.
Mesut Ozil doubled the advantage two minutes into the second half, with Hull goalkeeper Allan McGregor and his defence standing firm to keep the score respectable, while George Boyd should have grabbed a stoppage-time goal, but he could only head over from eight yards.
Hull ultimately failed to recreate the performance that led them to a stirring 3-1 win over Liverpool on Sunday, but Bruce refused to criticise his team's showing.
"Overall it was a difficult evening," he lamented. "We've had two tough games this week, but we've managed to pick up three points. That's a positive.
"I'm glad we still knuckled down, because we've avoided an embarrassing scoreline.
"Arsenal are a great team, and we showed resilience.
"The one thing you want when you come to the Emirates is to start well and they have scored a wonderful goal, we've been done on a one-two in a wide area, but it's wonderful.
"Arsenal are confident enough and then when they go 1-0 up early on it becomes a difficult evening for us.
"I was delighted to get back into the game but lo and behold we did the same thing in the second half but late on we rolled our sleeves up otherwise it could have been embarrassing."
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