Martinez scored in the 40th and 55th minutes for Atlanta (8-7-9, 33 points) to give him 85 career goals. He has eight in 16 games this season.
Cincinnati (4-11-8, 20 points) ended a 12-match winless streak in its previous outing but quickly fell behind in the fifth minute when Araujo made his first Atlanta goal memorable.
Playing in his fifth match since being signed as a Designated Player from French club Lille on Aug. 6, the Brazilian forward took a pass at midfield with his back to the goal.
He turned and dribbled past four players down the right channel, cut toward the goal and unleashed a left-footed shot from inside the box. Przemyslaw Tyton stretched and got his right hand on the ball but couldn't stop it.
Martinez doubled the lead as Araujo sent a free kick from 35 yards deep where Franco stuck out his right foot and redirected the ball to Martinez.
Atlanta nearly made it 3-0 just before the break, but Barco hit the right post and Araujo was denied on the follow-up by Tyton.
Martinez added the third goal after a timed run to receive a pass from Barco. Martinez has five goals in four career games vs. Cincinnati.
Barco got the final goal in the 86th minute with a direct free kick for his fifth goal of the season. Atlanta has seven goals in the past two games.
Brad Guzan made three saves for his seventh shutout of the season and Cincinnati was blanked for the 10th time.