Dan Kennedy made seven saves for Chivas, but a late rebound fell to the foot of Hainault, who blasted it past the goalkeeper for the defending Eastern Conference champions.
Chivas had its finest scoring chance in the 70th as second half substitute Ryan Smith fired in a cross to a waiting Juan Pablo Angel, who headed the ball just over the net of Dynamo goalkeeper Tally Hall.
Dynamo midfielder Brad Davis, the MLS assists leader in 2011, started for the first time since missing the MLS Cup in November because of a right quad strain.
