The Dynamo extended their unbeaten streak to four games after Brad Davis and Will Bruin scored in the first half and Oscar Boniek Garcia and Brian Ching added goals in the second.
United goalkeeper Bill Hamid received a straight red card in the 17th minute for bringing down Houston's Macoumba Kandji inside the penalty area, leaving backup Joe Willis hard-pressed to stop the one-sided onslaught.
The fifth-placed Dynamo, who had Davis and Ching net from the penalty spot, have now earned eight points from their past four games.
United entered the contest having won five of their past six league matches, but fall three points back of leaders Sporting Kansas City in the Eastern Conference.
At Red Bulls Arena, Fredy Montero came off the bench to score the equaliser for Seattle.
Alvaro Fernandez earned the visitors a 1-0 lead in the 16th minute with a volley off the left post but former Sounder Sebastien Le Toux snatched one back 24 minutes into his Red Bulls debut.
New York then surged ahead in the 61st minute through Joel Lindpere but Montero entered the match in the 62nd and beat Red Bulls goalkeeper Bill Gaudette five minutes later to leave the match tied.
The Red Bulls move past Chicago and into third place in MLS East, while Seattle remain third in the west.