The second leg of the total-goals series is Nov. 9 at New England. The winner plays New York or D.C. United for a spot in the MLS Cup.
Davis put the Revolution ahead in the 34th minute with a diving header off Kelyn Rowe's free kick, and Chris Tierney scored on a left-footed free kick from 23 yards in the 51st.
Davies added a second goal in the 78th minute, and Federico Higuain converted a penalty kick for Columbus in stoppage time.
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