With two outs in the ninth of a 3-3 tie game, Suzuki hammered a pitch from Tanner Scheppers (5-1) into the right field bleachers for a walk-off game-winner.
The blow handed a victory to Mariano Rivera (1-1), who tossed a scoreless top of the ninth as New York opened a three-game series with a victory.
New York starter Hiroki Kuroda went 6 2/3 innings, yielding three runs (two earned) on five hits, striking out six and walking one.
Leonys Martin launched a pair of bases-empty clouts for American League West-leading Texas.
Notable deaths of 2014 [PHOTOS]