Je-Vaughn Watson also scored for the Dynamo (8-9-12).
Andres Mendoza scored twice on penalty kicks for the Crew (11-9-8), getting the tying goal in the 64th minute and the go-ahead in the 76th.
''I'm very disappointed,'' Houston midfielder Brad Davis said. ''We clawed ourselves back in the game but two penalties - that's kind of hard to swallow.''
Mendoza's first goal came after a handball on Cam Weaver and the second when Watson kicked Dilly Duka in the stomach while the Crew player was attempting a shot.
Mendoza, who has five penalty kicks among his 11 goals, went left on his first try and right on the second against goalkeeper Tally Hall.
''I decided to go a different direction because I knew the 'keeper would go the same way where I shot it (the first time),'' Mendoza said.
Watson made it 1-0 in the 34th as Columbus was playing short-handed after Emmanuel Ekpo was given a red card in the 11th minute for hitting Adam Moffat in the face with his hand.
''Under the circumstances it was a great point at home,'' he said. ''Scoring two goals playing 79 minutes with a man down is great. The guys left everything on the field, scored two goals and almost got three points.''