The home side took the lead in the 31st minute, and it was a record-tying effort.
Martinez tied the MLS single-season scoring record with his 27th goal, taking advantage of a Columbus turnover near midfield before cutting onto his left foot and firing home.
Columbus struck back five minutes into the second half, however, as Gyasi Zardes collected a pass near the top of the box and buried a low shot into the far corner.
With 15 minutes to go, Atlanta grabbed the winner through Hector Villalba, who collected a long clearance and dribbled unmolested until reaching the box, where he drove past a defender and cut a low finish into the corner.
The home side put the game beyond doubt six minutes later when Martinez laid a pass off to Miguel Almiron, who placed a sidefooted effort past Zack Steffen in the Crew goal.
Luciano Acosta fired the home side in front after 12 minutes after getting on the end of a low cross from Paul Arriola.
United killed the game off just minutes from time, as Zoltan Stieber finished a breakaway after Revs midfielder Scott Caldwell had been sent off for his second yellow.