The game was scoreless until the 77th minute, when Clark kept his balance on a rain-soaked field after a pass from Brad Davis and directed the ball past New England goalkeeper Bobby Shuttleworth.
Boniek Garcia secured the crucial triumph with an insurance tally in stoppage time for the Dynamo (13-8-10), who stayed one point ahead of Columbus for the fifth and final Eastern Conference playoff spot with their 23rd straight home win.
The Revolution fell to 7-16-8.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys