The France striker outfoxed West Brom goalkeeper Russell Hoult to clinch the points after Francis Jeffers had cancelled out Danny Dichio's early goal for West Brom.
With Chelsea drawing 0-0 at home to Southampton, Arsenal lead the table with 42 points from 20 games, four more than their London rivals.
Elsewhere, struggling Bolton Wanderers gained a vital 4-3 victory over Newcastle United. Later on Thursday Liverpool entertain Blackburn Rovers and third-placed Manchester United visit Middlesbrough.
West Brom took a third-minute lead against Arsenal when Dichio powerfully headed home a corner, and the champions struggled to create openings for the rest of the half.
But they were level three minutes into the second period when Jeffers pounced from close range.
Jason Roberts then struck the post for West Brom but Henry, having missed on sitter, made no mistake with five minutes to go when Patrick Vieira charged down Adam Chambers's attempted clearance.
Chelsea wasted their chance to go top briefly when they were held by Southampton at Stamford Bridge.
Italian striker Gianfranco Zola struck the post and defender William Gallas blocked an effort by his own team mate John Terry in a frantic finale, but Chelsea had to settle for a point to extend their unbeaten league run to 11
THRILLING VICTORY
Bolton scrambled a thrilling victory at the Reebok Stadium, only their second home win in the league this season, thanks to two goals by Michael Ricketts.
Ricketts scored twice to give Bolton a 4-1 lead but Sam Allardyce's side were made to sweat as Shola Ameobi and Alan Shearer, with his second of the game, set up a nervy finale.
Bottom club West Ham's search for their first home win of the campaign continued after they drew 1-1 with Fulham.
Facundo Sava gave Fulham the lead but West Ham, who had Czech defender Tomas Repka sent off late on, earned a point through Trevor Sinclair's penalty.
Tottenham Hotspur recovered from two goals down at home to draw 2-2 against Charlton Athletic. Goals by Robbie Keane and Steffen Iversen hauled Spurs level after Jason Euell had scored twice for Charlton.
Spurs had wing back Christian Ziege sent off for the second successive game in stoppage time. The German was also red-carded against Manchester City on Monday.
