The Dynamo, who were beaten by the Los Angeles Galaxy back in December, looked set to open up with a stalemate until James Riley put the ball into his own net 10 minutes from the end.
Ricardo Clark then added a second in the 89th minute.
Graham Zusi, Oriol Rosell and Claudio Bieler scored as Sporting Kansas City came from behind to win 3-1 at the Philadelphia Union.
Sebastien Le Toux opened the scoring after 17 minutes, but Zusi levelled four minutes before the break and KC pulled away after the restart.
Second-half goals from Federico Higuain (51), Josh Williams (88) and Domenic Oduro (90) ensured the Columbus Crew got off to a positive start, winning 3-0 at Chivas USA.
Goncalves Jackson netted after 11 minutes to give FC Dallas a 1-0 win over the Colorado Rapids, Davy Arnaud's 35th-minute strike saw the Montreal Impact win at the Seattle Sounders by the same scoreline and the Vancouver Whitecaps were also 1-0 winners, over Toronto FC, thanks to Gershon Koffie's 59th-minute effort.