Drew, who left Tuesday night's game against Toronto in the third inning, batted seventh in Terry Francona's lineup for the second game of a three-game series with the Rays at Fenway Park.
"We waited until today, so he would be OK," Red Sox manager Terry Francona said before the game. "Again, with the turnaround [to a day game Sunday] ... we'll see how things go tonight for [Sunday]. Who knows, there may not even be a game."
Light rain fell in the area much of Saturday, but was gone in time for the Sox to take batting practice. Still, the outfield grass was wet, and the forecast for Sunday was for heavy rain.
"We'll kinda look at things, like we do after every game, and see about [Sunday's] lineup," Francona said.
Said Drew, whose injury was described as left quad tightness: "You have to understand your limitations. I've played long enough to know mine. There are things you have to be wary of."
Drew's return bolstered a less-than-healthy outfield picture, a picture that worsened Saturday night when rookie Brandon Moss underwent an appendectomy and will be out indefinitely.
Jacoby Ellsbury returned Friday night after missing three games with a sore groin, while Coco Crisp was dealing with problems in both legs.
Brandon Moss, who started three straight games with Drew out, was back on the bench Saturday night.
Francona said infielder Alex Cora, on the disabled list since April 16 with a sore right elbow, is progressing as he makes his way back.
After the game, the manager said Cora would accompany the team to Detroit and leave to play at Triple-A Pawtucket on Wednesday, Thursday and Friday.
"He's doing pretty well -- getting antsy, which I think is a good sign," the manager said. "Take ground balls and turn the double play today, go to short [Sunday] ... he's getting closer to letting it fly all the way. The biggest thing is he's starting to get a little antsy, which I think is a good sign."
Cora can come off the disabled list any time he's ready, while backup first baseman Sean Casey (hip) is on target to return next Sunday.
Mike Shalin is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.