Oakland evened the best-of-five series at one game each, but they left it late in a game dominated by both starting pitchers in the Coliseum in Oakland.
Both starting pitchers had excellent games, with Oakland's Sonny Gray going eight innings for four hits and nine strikeouts.
Detroit's Justin Verlander went seven innings for four hits and 11 strikeouts, but the bullpen couldn't finish the job.
Cespedes led off the ninth with a single to left field and then Seth Smith hit a single before Al Albuquerque intentionally walked Josh Reddick to load the bases.
Detroit manager Jim Leyland then brought in Rick Porcello to pitch to Vogt, who ended the game on the third pitch he faced.
Both managers heaped praise on A's rookie pitcher Gray, while not forgetting Verlander.
"I've got to give Gray a lot of credit. He was everything that was advertised," said Detroit's Leyland.
"We're not swinging the bats maybe the way we're capable but you can't take away anything form that performance tonight.
"He was real aggressive with electric stuff. He didn't back off at all. He came right at us. That's what the reports said. They said he'd go to his curveball when he got in trouble, which he did, but I was impressed with his fastball as well.
"Sometimes in a game like this you lose sight of how good Verlander was. He was vintage Verlander. This was post season pitching at its best."
The A's Bob Melvin was similarly impressed.
"You can tell (Gray's) excited about it. He's into every pitch," Melvin said.
"Runs seem to get tougher to come by when you go deeper and deeper in games like that and you had two starting pitchers who were just electric.
"They made big pitches when they had to. It just felt like one of those games where it was going to be a battle of attrition."
The series now moves to Detroit for Game Three on Monday. (Reporting by Andrew Both in Cary, North Carolina; editing by Amlan Chakraborty)
- Sports & Recreation
- Detroit Tigers
- Oakland Athletics
- Justin Verlander
- Yoenis Cespedes