But while the visitors had the better of things before the break, neither side really dominated.
Stephen Quinn nearly made it 2-0 when a half-volley went just wide from Ahmed Elmohamady's cross and Jay Simpson was denied by home keeper David Forde.
Millwall offered little, their best effort a hooked strike from Martyn Woolford that went wide.
But the second-half introduction of of Rob Hulse and Andy Keogh slowly began to make a difference and Henry shot high over the bar after being presented with a one-on-one opportunity by Robbie Brady's mistake.
The game at last began to open up in the final quarter.
Nick Proschwitz fired over for the visitors while at the other end, Woolford sent a free-kick just off target and Tigers goalkeeper David Stockdale made a decent save from Henry's low drive.
Robert Koren almost made it 2-0 late on but the visitors did not need the security of a second goal.
Millwall manager Kenny Jackett:
"I felt we put a lot of pressure on a very good Hull team. I think we were unlucky to lose the game and I felt we did well barring finding the goal.
"We need to make sure we play with that kind of effort, commitment and energy all of the time.
"We're still in the play-off mix - 16 games to go is a long time and we'll keep going."
Hull City manager Steve Bruce:
"We're unbeaten in seven away from home now but it is nice to get that first league win of the year.
"You have to show a bit of resilience in this league and we've done that again here.
"David Meyler has been a terrific acquisition for us. He's had a really good start to his career here, particularly when you consider he's had a few knee injuries. If he can stay fit, he'll be a big player for us."
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