(Reuters) - The Oakland Athletics built on their growing reputation of a team that refuses to give up with another ninth-inning rally that shocked the Detroit Tigers 4-3 on Wednesday and sent their playoff series to a decider.

Trailing 3-1 and on the brink of elimination, Seth Smith hit a game-tying RBI double and Coco Crisp delivered the winning single to give Oakland a second straight win at a rowdy Coliseum to even up the best-of-five AL Division Series at 2-2.

Crisp made a spectacular catch that sparked a 2-0 triumph in Game Three a day earlier, where the A's avoided being swept, and he came through again to set up Thursday's decider in Oakland.

Detroit had appeared on target for a berth in the American League Championship Series after starter Max Scherzer held Oakland to just one run on three hits in 5 1/3 innings.

Prince Fielder blasted a home run in the fourth, making up for being denied by Crisp's Game Three catch, for a 2-0 lead and the visiting Tigers added an insurance run in the eighth to re-establish a two-run lead.

However, a nervous-looking Jose Valverde was unable hold off the Athletics, who tapped into the inspired late-game play that has characterized their improbable run to the American League West title in the second half of the season.

The A's recorded an MLB-leading 14 walkoff wins in the regular season with the 15th setting up a winner-takes-all showdown for the right to face either the New York Yankees or Baltimore Orioles.

(Writing by Jahmal Corner in Los Angeles; Editing by John O'Brien)