Crisp scored with ease to cut Oakland's deficit to one, but Drew and third-base coach Mike Gallego took a chance.
The A's shortstop, who spent a good portion of this season and the second half of last year recovering from a broken ankle, didn't stop at second base.
When Tigers center fielder Austin Jackson fielded the ball off the base of the wall and relayed to second baseman Omar Infante, who delivered a strike to Detroit third baseman Miguel Cabrera, Drew was tagged out and the A's rally was squelched until the pivotal ninth.
From where the A's sat in the dugout and bullpen, it was a risk they expected to take, considering how aggressive they've been all season.
"He hit the ball in the gap," reliever Sean Doolittle said. "They've got to run a long way to catch it. The grass in the outfield is slick. That ball's going to be wet when he gets it. It's going to take a perfect relay throw to get him. We're going to put the pressure on them and make them make the play. I mean, they made a great play. But that's the aggressiveness that we're all about. Absolutely."
Gallego explained the decision as a sort of perfect storm. Drew was going and Gallego wasn't going to tell him to stop.
"That's a play that the ball's in front of the runner and you've got a split-second to make the decision and it's usually made by the runner," Gallego said. "He peeked at me, I was bringing him, I saw the ball scoot pass Jackson, go to the wall, and obviously the cardinal sin is not to make the first out or the last out at third base.
"It wasn't a good call. It wasn't a good play. But at the time, I felt I couldn't stop him, either. If I stopped him, I would've left him hung out to dry on the basepaths. So he made his decision, I made my decision, and we ran with it. And it didn't work out."
Naturally, the A's stirring ninth-inning rally, in which they scored three runs off Detroit closer Jose Valverde to extend the series to a winner-take-all Game 5 on Thursday night, ensured that the miscue on the bases would be rendered a moot point.
But the A's sounded like they'd have no problem if Drew did it again.
"It's just a part of the game," starter A.J. Griffin said. "We're playing hard, we want to win, and we're going to do things like that. It's unfortunate he got thrown out, but we still got it done in the end.
"It's part of baseball. We were still pumped in the dugout after that. We were chipping away. We trust in ourselves and we know we're going to get another shot. We capitalized on it in the ninth, and it was great."
Gallego agreed with that sentiment.
"That's the type of baseball we play here," he said. "We're going to try to be aggressive all the time, and sometimes we're going to err on the aggressive side, and being aggressive around here has also won us a lot of games.
"There's times where being overaggressive looks like the wrong decision, which I'm sure it looked like for a few innings there, and we all felt it, but in this game you can't get down."