Columbus (5-6-5) avenged last season's conference semifinal 7-3 aggregate loss to New England (6-6-6), which has lost four straight on the road and nine of its last ten games.
Kamara scored the winner with his heal in the 50th minute for his 12th goal of the season.
New England's Lee Nguyen scored in the first 35 seconds, drilling in a shot from the top of the 18-yard box.
The Crew answered right back in the fourth minute. Hector Jimenez's header shot hit the crossbar and bounced to Kamara. Kamara fired a header that bounced to the left of goalkeeper Bobby Shuttleworth and into the back of the net.
Charlie Davies, who leads the Revolution with seven goals, took only one shot.
Goalkeeper Steve Clark made his 50th career start for the Crew.