The win ended a five-game winless streak for New England (8-15-5) and snapped Houston's two-game unbeaten streak.
Dube got a cross from Ilija Stolica from the left and put a one-timer by Houston goalkeeper Pat Onstad from 10 yards to give New England the 2-1 lead.
Dominic Oduro tied the score in the 60th minute on a one-timer from 8 yards on the left after getting a cross from Richard Mulrooney and nailing it into the net.
Shalrie Joseph gave the Revolution a 1-0 lead in the 43rd minute after getting a pass from Emmanuel Osei in the box, dribbling it to the right and then firing it past Onstad and into the left net.
Oduro nearly tied things in first-half stoppage time, but his shot from 10 yards in the middle of the box was stopped by a diving Bobby Shuttleworth.
Houston (7-15-6) finished the game two men down after second-half sub Joseph Ngwenya was given a straight red card in second-half stoppage for a hard tackle, and Geoff Cameron was given a straight red for a forearm to the face of Jason Griffiths later in second-half stoppage.