Escobar came up favoring his left quadriceps after hitting into a fielder's choice in the 10th inning and got lifted for a pinch-runner.
Myers hurt his right wrist in a center-field collision with Desmond Jennings on A.J. Pierzynski's triple that drove home the winning run in a 3-2 Red Sox win.
"Escobar has a little thing with his quad, nothing horrible," Rays manager Joe Maddon said. "Might be able to play [Sunday], Monday at the worst. Possibly do some pinch-hitting, whatever, tonight. But to actually play [Sunday] or the next day."
Myers wore a protective brace over his right wrist Saturday afternoon and was expected to be examined by a doctor before Saturday night's game.
When asked about the injury, Myers noted that he learned from watching the replay that he landed on his glove hand after running into Jennings.
"And my right hand came down and slapped the ground," Myers said. "It's a little cut up from where I hit the ground."
When asked if he was feeling pain in his wrist, he replied: "It doesn't feel good. It's sore. It's definitely sore."
Maddon said "honestly I don't want to even want go there yet" when asked about his concern level regarding Myers.
"It could be something very minor and insignificant, I'm not sure, once it gets checked out, I'll know more," Maddon said. "It's really hard to create conjecture. It could be something, it could be nothing. Let's just see what the doctor says."
Ben Zobrist, who just returned from the disabled list Friday, started at shortstop Saturday night. Maddon felt fortunate about that fact given that Zobrist has played a lot of short.
"We could have covered that in a lot of ways, but it's nice to get Zo back," Maddon said. "We still have a lot of flexibility and versatility among the group. He's at the center of that."
Kevin Kiermaier started in right. The rookie outfielder plays mostly center, but he has experience in right.
"I feel comfortable out there," Kiermaier said. "I'll be ready to go tonight. I'll get out there and make sure to check out everything so I know how the balls come off the walls and everything. And really get my work in during batting practice."
Kiermaier has not played at Fenway, which has odd outfield configurations, to say the least.
"Yeah, I was talking to Wil about that [Friday] and he said that wall in right is real tricky down there," Kiermaier said. "And it's real short down there, especially where the Pesky Pole's at. I'll do the best I can to prepare myself and be ready for anything once it's game time."