With each pitch in the late innings creating drama befitting the significance of the occasion, the Tigers won the fifth and deciding contest in the post-season's opening round and will meet the Texas Rangers in the best-of-seven American League Championship Series.
Game 1 of that confrontation will be played Saturday in Texas, with the Rangers trying to win their second league title in as many years.
The Tigers fought off New York the rest of the way despite putting themselves in situations where the Yankees could have turned the game around with a single swing of the bat.
New York twice left the bases loaded, once in the fourth inning when starter Doug Fister retired Russell Martin and Brett Gardner on pop fly balls to escape the jam. It was in the seventh inning, however, that the Yankees missed a huge chance to take the lead.
Benoit came on in relief of Max Scherzer with one out and one on and the Yankees promptly filled the bases on a single by Curtis Granderson and a slow ground ball from Robinson Cano that Benoit misplayed into an infield hit.
Valverde, who had 49 regular-season saves, appeared in the ninth and retired the side in order. With the New York crowd screaming for a rally, Granderson flew out to left, Cano lined out to center while breaking his bat and Rodriguez again struck out swinging.
It was the second straight year Rodriguez recorded New York's final out of the season with a strikeout. He did the same thing when the Yankees were eliminated in Game 6 against Texas in last year's ALCS.
New York starter Ivan Nova left the game after two innings with a strained forearm.
Young was taken out for Detroit in the seventh with what was described as a pulled muscle in his left side.