The New York Red Bulls were playing a man down in 100-degree heat and down a goal in the final five minutes at Red Bull Arena on Saturday.
Juan Agudelo put New York in front late in a lackluster first half, but two goals after the break from Marvin Chavez had the visitors ahead.
Dane Richards was sent off 10 minutes from time with New York still trailing by a goal, but Henry's league-leading 11th tally of the season allowed the hosts to claim just their second point from the last four games.
Agudelo opening the scoring in the 39th minute.
Richards played a low cross into the penalty area from the right wing, and Agudelo tried to redirect the ball toward goal. The striker didn't catch it clean, but the ball took a deflection off of a Dallas defender and looped inside the far post past goalkeeper Kevin Hartman.
Dallas started quickly in the second half and equalized within six minutes as Ricardo Villar played a ball into the area for Chavez, who also benefited from a deflection as his shot made its way past goalkeeper Frank Rost.
Chavez then had a close-range shot saved by Rost before Richards sent a 25- yard rocket off the post for New York one minute later.
The Hoops took their first lead in the 78th minute when George John knocked down a free kick inside the box for Chavez to fire home, while Richards picked up a second yellow card a few minutes later for a clumsy tackle from behind.
But Henry stepped forward in the last five minutes to equalize as he brought down a ball with his back to goal, cut back past a defender and curled a left- footed shot past Hartman.
The Red Bulls are next in action when they take part in the 2011 Emirates Cup at the Emirates Stadium in London, England on July 30 and 31. On Saturday, July 30 the Red Bulls face off against French club Paris St Germain (9 a.m. ET; TV: MSG). The following day, the Red Bulls take on Henry's former club, Arsenal FC (11:20 AM ET; TV: Fox Soccer Channel). New York returns to MLS action on Saturday, August 6 at Real Salt Lake at 9 p.m. ET (TV: MSG).
-- Sports Network contributed to this report