Resop was placed on the disabled list June 16 after suffering a strained left oblique. He had allowed five runs on five hits in two innings of relief in his only appearance for Atlanta this season.
A fourth-round pick by the Marlins in 2001, Resop is 3-3 with a 6.14 ERA in 58 career games in the Major Leagues.
Resop, who allowed one hit over five scoreless frames in his last start for Gwinnett on June 10, faced one over the minimum in his five innings of work.
He retired 10 straight after issuing a two-out walk in the first to Red Wings' left fielder Brian Dinkelman. After walking former Major Leaguer D'Angelo Jimenez to start the fifth, Resop got Jacque Jones to fly out and induced a double play from Matt Marci to end the inning.
Brian Beachy, who fanned 13 earlier in July for Double-A Mississippi, allowed a leadoff walk to open the sixth before striking out the side. Dinkelman broke up the no-hit bid with a single to begin the seventh.
Beachy picked up the save in his Triple-A debut, whiffing seven while allowing three runs on five hits over four innings.
Freddie Freeman slugged a two-run homer and Matt Young doubled, singled and knocked in two for Gwinnett. Brandon Hicks was 3-for-4 and scored twice.