Garcia snapped a 2-2 tie by swatting an inside fastball from right-hander Michael King (1-4) slightly above the knees deep into the left field seats for his 17th homer to score Nathaniel Lowe.
Garcia reached 60 RBIs while sending Texas to its fifth win in six games and fourth win in five meetings over the Yankees this year
The Rangers Joe Barlow (1-0) stranded Anthony Rizzo on base in the ninth to set up Garcia's latest clutch hit. Texas left-hander Will Smith delivered a 1-2-3 10th inning for his 14th save in 15 chances
The Yankees lost for the 10th time in 16 games since losing slugger Aaron Judge to a bruised right toe
The Rangers Mitch Garver had an RBI single in the eighth off Clay Holmes for a 2-1 lead before Kyle Higashioka batted for Oswaldo Cabrera and hit a tying sacrifice fly off John King
Billy McKinney, who was lifted for Donaldson in the 10th, had an RBI groundout in the second that scored Rizzo.
Texas tied it in the fourth inning by capitalizing on shoddy New York defense.
Ezequiel Duran had a two-out an infield single, advanced to third on a single by Leody Taveras then scored when the hit dropped between Volpe and center fielder Isiah Kiner-Falefa resulting in an error.
Texas starter Dane Dunning allowed two runs on five hits in seven-plus innings. The right-hander struck out two, walked two and was aided by his defense turning three double plays.
New York starter Clarke Schmidt allowed an unearned run on six hits in 5 1/3 innings. Schmidt struck out three and walked one.
--Field Level Media