Luiz Araujo also scored his third of the year for Atlanta (5-5-4, 19 points) in the first game for both teams since the end of May due to the June international match window.
Araujo and Martinez also assisted each other's goals as Atlanta United won for just the second time in nine matches.
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Inter Miami were shut out for the fourth consecutive time on the road while being outshot 18-12 overall and 8-3 in efforts on target.
Martinez now leads Atlanta with 92 all-time MLS goals since joining the club for their expansion 2017 season.
But the Venezuelan international has not produced at the same rate since he missed nearly all of the 2020 season recovering from a torn ACL suffered in the campaign's first week.
He had surgery on the previously injured knee in early April and made his return to the field as a halftime substitute in Atlanta's final game before the break, a 2-1 loss to Columbus on May 8.
He got his first start since then on Sunday and contributed his third assist of the year when he drew a double team just beyond the penalty area in the fourth minute.
Martinez looked right and found Araujo, who guided a crisp left-footed finish into the bottom left corner from about 25 yards out.
Araujo returned the favor on one of Atlanta's better sequences of the second half.
Araujo reached the rebound and instead of trying for a second goal himself, looked right to find Martinez, who snapped in a first-time finish to put the game out of reach.