Ryan Johnson put the visitor ahead after six minutes but Red Bulls' Marcus Holgersson levelled seven minutes later before two goals from Kenny Cooper and Henry's effort in the last minute sealed a comprehensive New York win.
Two goals from Steven Lenhart saw San Jose Earthquakes twice come from behind to secure a 3-3 draw against FC Dallas.
Alan Gordon put the Earthquakes ahead in the 24th minute, but Dallas' Blas Perez levelled the score after 37 minutes and found the back of the net 18 minutes from the end to put his side ahead.
Lenhart, who came off the bench early in the second half, scored an equaliser after 82 minutes.
Matt Hedges looked to have sealed the win for Dallas when he found the back of the net in the 88th minute, but Lenhart notched a second equaliser in the dying moments to secure the draw for the Western Conference leader.
Alvaro Saborio scored a hat-trick as Real Salt Lake won 4-0 at Chivas USA. Paulo Junior found the back of the net to notch Salt Lake's fourth.
A 0-0 draw at Vancouver Whitecaps was enough to send Seattle Sounders into the MLS play-offs.
Milovan Mirosevic scored two minutes from time to secure a 3-2 win for Columbus Crew over Philadelphia Union.
Jairo Arrieta's quickfire double at the end of the first half had put Columbus in control, but Philadelphia fought back with a penalty from Danny Cruz in the 65th minute and an 86th-minute equaliser from substitute Jack McInerney.
Chinedu Dike equalised late in the match to land Portland Timbers a 1-1 draw against DC United, who had taken the lead through Chris Pontius' penalty on the hour mark.
Elsewhere, Ricardo Clark and Oscar Garcia were on target in Houston Dynamo's 2-0 win over New England Revolution.