"He was a little stiff going out for that inning and it looked like the velocity dropped," Oakland manager Bob Melvin said. "We weren't going to let that go on any more. We have to be careful with him."
David Cooper hit a tying homer in the ninth inning and Edwin Encarnacion scored on catcher George Kottaras' throwing error in the 11th, lifting the Toronto Blue Jays over the Athletics 3-1 Saturday.
The Blue Jays ended a six-game losing streak a day after they fell to the A's 5-4 in 15 innings.
"You're not going to win all those games, yet you expect to," Melvin said. "We didn't come through this time."
Griffin said he started feeling something when he went out to warm up.
"I thought it was something I could just work through but it kept grabbing at me," Griffin said. "It was something that I could not get loose today."
The A's had won three in a row. They loaded the bases in the 10th, but Josh Reddick was called out on strikes.
Oakland went into extra innings for the sixth time in its last 24 games, a span that includes a pair of 15-inning wins.
"I guess you can't walk every game off," said A's third baseman Brandon Inge, who had a 13-game hitting streak end.
Jesse Chavez (1-1), promoted from Triple-A on Friday, got the win and Darren Oliver recorded his second save.
Griffin, who lowered his ERA to 2.42, allowed a leadoff single to Yunel Escobar and then retired five straight before being replaced by Jordan Norberto, who gave up four hits over a career-high 3 2-3 innings.
Derek Norris hit an RBI double in the Oakland second. The A's loaded the bases with two outs in fifth but Ricky Romero struck out Michael Taylor.
Sierra was thrown out at the plate trying to score on Anthony Gose's two-out double in the second.
The Blue Jays also had two runners in scoring position in the fourth before Norberto got Yan Gomes on a short flyout and Sierra on a grounder.
NOTES: Davis extended his hitting streak to a season-high nine games. ... LHP Aaron Laffey (2-2, 4.20) goes for the Blue Jays in Sunday's series finale against LHP Tommy Milone (9-8, 3.68). ... The A's became the first AL team to win a pair of 15-inning games on the same homestand. ... Oakland is 9-3 in extra-inning games.