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The French forward struck three minutes before half time, coolly finishing with a low shot after Sylvain Wiltord and Ashley Cole had split City's suspect defence.
It was Arsenal's 26th league game without defeat.
Manager Arsene Wenger said after the match: "This shows the consistency and intensity in the side. There's a tremendous spirit in this team."
Wenger and Henry also had words of comfort for City, who finished with ten men after Ali Benarbia was sent off for a second yellow card, six minutes from time.
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"City are a good team," added Henry. "They had the courage to have a go at us and made it difficult."City manager Kevin Keegan gambled on a high risk strategy of attacking Arsenal. He gained his reward in the 28th minute when ex-Gunner Nicolas Anelka headed in Benarbia's right-wing cross to equalise the prolific Wiltord's opener three minutes earlier.
City finished with ten men after Benarbia was sent off for a second yellow card, for dissent.
"We can play better, we can pass better," Keegan said after the match.
"We created problems for ourselves. They pressed us hard and profited from it.
"This was a big test for us and we didn't come through it. Anelka did terrific back here. He's a quality player.
"But he didn't get a lot of help from the other forwards. I thought Benarbia's sending off was very harsh. There must be question marks over the linesman."
Arsenal also had a complaint. An offside decision denied Henry their third goal after he crisply finished Dennis Bergkamp's flick. TV replays proved Henry's contention that: "I was onside when the ball was played."