Henry's double to defeat spirited Southampton extended Arsenal's lead at the top of the table to five points over Manchester United.
The Frenchman, who scored his first premier league goal against Southampton in September 1999, reached the milestone on 31 minutes before netting again in the last minute to seal the points.
Arsenal, who advanced their club record unbeaten start to the league season to 25 games, have 61 points. On Wednesday, United host League Cup finalists Middlesbrough while Chelsea, in third, visit Portsmouth.
"It was a tough game and Southampton played very well and closed us down well all over the pitch," Wenger told Sky Sports.
"Overall we kept a clean sheet and that is very positive because we know we can always score another one. It came very late but it was a relief I must say."
Wenger's side, which included Spanish striker Jose Antonio Reyes making his first league start in place of injured Dennis Bergkamp, were never allowed to dictate affairs at Highbury.
Robert Pires twice tested Antti Niemi early on but Saints forced a flurry of corners and Lauren was forced to head one off the line.
Henry made the breakthrough when, with a hint of offside, he raced on to a pass from Pires and his shot was strong enough to beat Niemi.
Arsenal keeper Jens Lehmann made two fine saves early in the second half to deny Brett Ormerod and substitute Chris Baird as Saints took the game to the hosts.
But they could not find an equaliser and Henry made sure of the points when he controlled another Pires cross and picked his spot in the top right corner.
Leeds United moved off the bottom and relegated Wolverhampton Wanderers back to the foot of the table with a 4-1 demolition of their fellow strugglers at Elland Road.
Victory ended a run of seven successive defeats for debt-laden Leeds, who were handed another extension last week to solve their financial crisis and avoid going into administration.
An embarrassing blunder from Leicester City goalkeeper Ian Walker handed visiting Bolton Wanderers a share of the spoils in a 1-1 draw in Tuesday's other match.
Les Ferdinand fired struggling City ahead but Walker, having gathered an effort from Kevin Davies, let the ball slip out of his grasp and it rolled under his body and into the net.
