Miles Robinson tied the score on a header off an Ezequiel Barco corner kick in the 70th minute for Atlanta (13-9-12, 51 points), which officially clinched a playoff berth. The Five Stripes finished with the fifth seed in the Eastern Conference.
Zico Bailey scored his first career goal for last-place Cincinnati (4-22-8, 20 points), which concluded its season with 12 consecutive losses.
Martinez's winner came after Jurgen Damm's cross was headed high into the air by Cincinnati defender Tyler Blackett. Martinez settled under the ball at the top right of the 6-yard box and put a sidewinding volley past goalkeeper Kenneth Vermeer and into the far side netting. It was Martinez's team-leading 12th goal of the season in just 24 appearances.
After trailing 1-0 at halftime, Atlanta made an all-out push in the second half. Vermeer was forced to make a kick save on a 10-yard shot by Martinez in the 53rd minute and Robinson put a header off the right post on a free kick by Barco in the 66th.
Cincinnati opened the scoring in the 21st minute. Haris Medunjanin tried to work back and forth at the top of the 18-yard box but was stifled by three defenders. He passed the ball wide to Bailey on the right wing, who worked a give-and-go with Luciano Acosta near the top right of the penalty area. Acosta sent a back-heel pass to Bailey, who was cutting toward the center of the field, and he curled a low, left-footed shot that got past diving Atlanta goalie Brad Guzan and just inside the left post.
Bailey, a 21-year-old homegrown defender, was making his 16th career MLS appearance.
Acosta had a good chance to score in the third minute, but Guzan was able to tip the shot over the crossbar. Guzan also made a diving save of a Medunjanin attempt in the 36th minute.
The only save Vermeer had to make in the opening half came on a shot from outside the 18-yard box by Barco in the 25th minute.
Both goalies were credited with two saves.