A day after seeing KC pull three points clear of them, United got off to a terrible start as Hamid rushed out to challenge Mac Kandji in the 17th minute, giving away a penalty and seeing red in the process.
Brad Davis beat substitute goalkeeper Joe Willis with his spot-kick and Will Bruin tapped in a second eight minutes before the break.
Boniek Garcia headed his first MLS goal after 62 minutes and Brian Ching converted the Dynamo's second penalty when Calen Carr was fouled by Danny Cruz in the closing moments.
Sebastien Le Toux scored on his New York Red Bulls debut as his new side drew 2-2 with the Seattle Sounders.
Two days after joining fellow Frenchman Thierry Henry in New York, Le Toux scored in the 24th minute to cancel out Alvaro Fernandez's 16th-minute opener for Seattle.
Joel Lindpere put New York ahead in the 61st minute, but the lead lasted just six minutes before Freddy Montero struck.