Finlay neatly headed home a left-footed cross from Waylon Francis in the 54th minute for his seventh of the season as the Crew rallied from two goals down.
Houston's Brad Davis served a corner kick and A.J. Cochran appeared to head it to the far post for what would have been his first MLS goal. Upon review, it was determined defender Aaron Schoenfeld deflected the ball, so it went down as an own-goal against Columbus (9-9-10).
The Crew's Wil Trapp scored his first MLS goal to cut it to 2-1 in the 48th.