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.
Workers accuse National Zoo of animal mismanagement
Couple calls 9-1-1 over missing hash browns; assault McDonanld's employees