With time winding down, Moffat took a pass from Corey Asche and unleashed a hard shot into the net.
With the tie, the sixth-place Dynamo (10-8-7) prevented seventh-place Chicago from bypassing them for an Eastern Conference playoff position.
The Fire (10-10-5) got their only tally on an own-goal by Houston's Bobby Boswell in the 37th minute.
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