The Frenchman, who netted in the 73rd minute, was given his marching orders in injury time when he was involved in an off-the-ball incident with Adam Moffat in an exhilarating affair at JELD-WEN Field.
Austin da Luz opened the scoring with the Red Bulls in the 5th minute before the Timbers struck three times through Jack Jewsbury, Kevin Goldthwaite and an own goal from Stephen Keel.
Henry scored his eighth goal of the season with a neat left-footed finish to make it 3-2 before Jewsbury hit the upright from the penalty spot, denying the Timbers a two-goal lead.
And it proved to be a crucial miss as Timbers teammate Rodney Wallace handballed in the area and Dwayne De Rosario stepped up to the plate to send home the equaliser in the 96th minute.
The draw kept the Red Bulls on top of the Eastern Conference table whilst the Timbers dropped to seventh in the West.
In other MLS matches, Sporting Kansas City defeated San Jose Earthquakes 1-0, Seattle Sounders scored a late winner to take down Toronto FC 1-0, New England Revolution and Chicago Fire drew 1-1, Columbus Crew won 2-0 at Houston Dynamo, Real Salt Lake and DC United played out a 1-1 draw, Vancouver Whitecaps scored their second win of the season with a 1-0 result over Philadelphia Union and FC Dallas beat Chivas USA 2-1.
2011 MLS season - Week 14 scores
Portland Timbers: 3 (Jack Jewsbury 48', Kevin Goldthwaite 49', Stephen Keel (og) 67') New York Red Bulls: 3 (Austin da Luz 5', Thierry Henry 73', Dwayne De Rosario (p) 90+5', red card: Henry 90+3') JELD-WEN Field, Portland, OR - 18,627