Columbus hit back when Hector Jimenez lifted the ball into the box for Kamara, but his headed effort hit the bar. Federico Higuain gathered the rebound, but also saw his strike crash off the woodwork and bounce over the net.
The home side took the lead just before the break when they won a free kick on the edge of the box and Bobby Burling curled his strike over the wall and into the top corner.
Kamara notched his second goal of the game to hand the visitors the lead when he converted Jimenez's low cross from the left after Tchani had released the run of the full-back down the wing.
Steve Clark kept his side ahead when he made an impressive stop to deny Doyle an equaliser in the dying minutes as he stretched out to palm the ball away from goal.
The keeper made another fine save to secure the victory for his side when he blocked an effort from Dillon Serna, while the game ended on a sour note for the Rapids as they were reduced to 10 men when Axel Sjoberg was dismissed for a second bookable offence.