The A's rode a major league-leading 14 walkoff wins in the regular season to an improbable AL West title. Those paled in comparison to No. 15, which set up a win-or-go-home Game 5 against Justin Verlander and the Tigers.
Reddick led off the ninth with a single just under the glove of diving second baseman Omar Infante. Josh Donaldson followed with a double off the wall in left-center and both runners scored on Smith's double.
"There's a confidence," manager Bob Melvin said. "We've done it so many times so there's always going to be that confidence until we make that last out."
Two outs later, Crisp lined a single and Smith scored easily when right fielder Avisail Garcia couldn't handle the ball.
That set off a raucous celebration near first base as the A's poured out of the dugout to mob Crisp, who was the recipient of a whipped cream pie that became a regular occurrence in this remarkable season in Oakland. This marked the second time the A's erased a two-run deficit in the ninth inning to win a postseason game, the other coming in Game 5 of the 1929 World Series.
"It's amazing," Crisp said. "The guys in front of me obviously did a fantastic job of getting on base. ... This club, we've been battling the whole year, giving 100 percent, and these walkoffs have been our MO this year."
Ryan Cook retired four batters for the win.
The A's, who have the lowest payroll in baseball, need just one more surprising result to win their second postseason series since 1990. Rookie Jarrod Parker will take the mound in Game 5 on Thursday night against Verlander, the reigning AL Cy Young winner and MVP.
"That's why this is the greatest game of all," Tigers manager Jim Leyland said. "It looked like we were going to get it. We didn't do it. We didn't quite get the 27 outs, that's part of the game. You get tested all the time in this game. And this is a good test."
The Tigers looked to be in prime position to advance to their second straight ALCS and have a rested Verlander for Game 1 when they took a 3-1 lead into the ninth behind a strong start from Max Scherzer and a homer from Prince Fielder.
Now the A's are one win away from repeating last week's three-game sweep of Texas that gave them the AL West title on the final day of the regular season. After losing the first two games in Detroit, the A's won 2-0 in Game 3 and are looking to become the eighth team to rally from two games down to win a best-of-five series.
The San Francisco Giants will have a shot to do it as well earlier Thursday when they face Cincinnati in Game 5 of their NL division series.
Scherzer, who was dealing with shoulder, deltoid and ankle injuries late in the season, looked in top form against the A's. He allowed just one baserunner in the first four innings and struck out seven of the first 15 batters before running into his first trouble in the fifth.
Smith worked a two-out walk and went to third on Derek Norris' opposite-field blooper down the right-field line. But Scherzer responded by getting Cliff Pennington to chase an offspeed pitch in the dirt for his eighth strikeout.
The A's finally got to Scherzer for an unearned run in the sixth. Crisp reached when Fielder misplayed a hard grounder to first base into a two-base error. Crisp advanced on a wild pitch and scored on Stephen Drew's double to right-center. But the A's ran themselves out of a potential big inning when third-base coach Mike Gallego waved Drew around to third, where he was easily caught on the relay for the first out.
Octavio Dotel and Phil Coke both retired a batter to get out of the sixth and Al Alburquerque pitched a perfect seventh in his first appearance since his memorable kiss of the baseball on a comebacker by Yoenis Cespedes in Game 2. Joaquin Benoit escaped a first-and-second jam in the eighth by striking out Brandon Moss, but Valverde couldn't close it.
"This is the toughest moment in my whole career," Valverde said. "I had everything. These guys hit it. There's nothing I can do."