In his previous two outings, Archer had been rocked by the Red Sox and Yankees for nine combined earned runs on 15 hits in seven innings, unable to record more than 12 outs in both games.
"It was good to see [Archer] bounce back," Rays manager Kevin Cash said. "He's had some rough starts here [lately]."
The Rays' righty exited after the first two White Sox batters took him deep on Sept. 2 in Chicago. He pulled himself because his arm didn't feel right, and team doctors later diagnosed him with right lateral forearm tightness, breathing a sigh of relief it wasn't more serious.