Cooper scored in the third and 13th minutes to give him six goals this season, and Henry added goals in the 40th and 90th to regain the MLS goals lead with seven.
''It's always good when the team can get an early goal,'' Cooper said. ''Fortunately, we were able to do it again today. We've done it a couple times this year. We got off to a great start and I thought from beginning to the end, it was a real solid performance.''
The two forwards have scored all but one goal this season for the Red Bulls (3-2).
New York won its third straight behind rookie goalkeeper Ryan Meara. He had seven saves but lost his shutout in the 89th minute when Chad Marshall scored on a header off Kirk Urso's corner kick.
''I thought we played a great first half,'' Henry said. ''I don't think we played well at all in the second half.''
It didn't take long after the Crew goal for Henry, whose goals have come in the past three games, to silence what was left of a crowd of 11,516 at Crew Stadium when he found himself in a familiar position throughout the game - alone in front of the goal.
He calmly settled a service from the left flank by Joel Lindpere and used a clinical finish to cap the match against what had been a stingy defense coming into the meeting of Eastern Conference teams.
The Crew (2-2) had shutouts wins in their previous two matches, but Cooper ended that streak early off an assist by Henry, in his first match at Crew Stadium.
Henry sent a long ball into box where Cooper shielded the ball from defender Eric Gehrig, turned and fired a shot past goalkeeper Andy Gruenebaum.
''I think we played against a very good team,'' Crew coach Robert Warzycha said. ''We didn't do much to stop them scoring goals.''
- Thierry Henry
- Kenny Cooper
- New York Red Bulls
- Columbus Crew