However, on the stroke of half time, Henry found himself in position to score and the ex-Arsenal frontman coolly stroked the ball beyond the reach of Clark to restore New York's advantage.
With 11 minutes played in the second period, Henry turned provider for Lloyd Sam, who scored a third for the Red Bulls and put daylight between the sides.
The Crew's hopes of a comeback were dashed when Bernardo Anor was sent off for fighting late in the game.
Victory was sealed in stoppage time when Alexander added a fourth for the side from the Big Apple.
New York are now up to third in the Eastern Conference, while Columbus languish in eighth place.