Moffatt got the winning tally when his shot rebounded off the back of Revolution goalkeeper Bobby Shuttleworth and found its way into the net, snapping a 1-1 tie.
The Dynamo midfielder also tallied in the 49th minute as Houston (8-6-5) notched a second straight victory following a seven-game winless streak.
Saer Sene scored for New England (6-6-6), which came into the game in sixth place in the Eastern Conference.
Sign language interpreter at Mandela service called out as fake on Twitter
Puzzle-maker slips 'Murdoch Is Evil' into Rupert Murdoch's Sunday Telegraph