Henry took a pass from Tim Cahill before firing a shot into the bottom right corner in the 57th minute after Joao Plata's 18th-minute strike had put New York behind.
The result dropped New York out of the play-off spots in the Eastern Conference, but the former Arsenal star took the positives out of a draw against a side who have proved tough opponents in recent seasons.
“Usually we come here and we lose," said Henry.
"It’s a draw. We’re not extremely happy with it but sometimes you have to save something out of a game and we did that.
"It wasn’t one of our best games, but sometimes you have to get a result like that away from home, especially in a place like Salt Lake."
Meanwhile, DC United goalkeeper Bill Hamid was in impressive form as he secured his fifth clean sheet of the season in his team's 3-0 victory over Toronto FC, the Washington side's fourth straight win.
Eddie Johnson and Chris Rolfe goals - plus an unfortunate own goal from Nick Hagglund - sealed the win.
New England Revolution ended their eight-match losing streak as they beat Colorado Rapids 3-0, with Lee Nguyen to the fore.
Nguyen's shot deflected off Drew Moor for an own goal after 10 minutes, the first time New England had been ahead on the scoreboard since May 24.
Colorado's Thomas Piermayr was sent off for his second yellow card on 74 minutes and Nguyen cured in the resulting free-kick from the edge of the box. Four minutes later, Nguyen provided the assist for Kelyn Rowe to score.
The Vancouver White Caps played out a goalless draw with the Chicago Fire, with Vancouver's Erik Hurtado missing his side's best chance of the game.