Other than a couple of big swings by Josh Hamilton, he was up to the challenge.
Garcia worked around two homers by Hamilton to remain undefeated against Texas for eight years, and the New York Yankees beat the Rangers for the third straight night, 3-2 on Wednesday.
The Yankees have held the American League's best offense to only four runs in the first three games of the four-game series.
"Our guys have done a tremendous job," Yankees manager Joe Girardi said. "I applaud our pitchers."
Hamilton became the second player to reach 100 RBIs this season -- Detroit's Miguel Cabrera was first -- with his career-high 33rd homer, a line drive to right in the fourth inning. His majestic drive in the sixth was all Texas could muster in its eighth straight loss in the Bronx.
With a chance to tie the game in the ninth, Hamilton was struck out by Rafael Soriano.
"When you're seeing the ball good, you feel like you can pretty much hit anything," Hamilton said. "But, at that point in the game, you just want to get somebody on base and give yourself a chance to tie the ballgame up."
Nick Swisher gave the Yankees the lead with an RBI double off Scott Feldman in a three-run third inning. Swisher put the Yankees ahead in the first two games, too. He hit a grand slam Monday and a two-run shot Tuesday night in a matchup between the teams with the best records in the AL.
Garcia (7-5) followed Kuroda's two-hitter Tuesday by giving up four hits in 6 2/3 innings of a game delayed by rain at the start for 1 hour, 45 minutes.
Garcia has not lost to the Rangers since 2004, going 5-0 with a 1.90 ERA in seven starts.
"When you see one guy pitch and the other guy pitch, you're thinking you got to go out there and try to do the same," he said.
A well-rested bullpen then finished for the Yankees' seventh win in eight games.
With second baseman Robinson Cano getting a night off because of a stiff neck, Mark Teixeira serving as the designated hitter and Alex Rodriguez out with a broken hand, Derek Jeter was the only regular in the infield, and the Rangers tested the group in the fourth inning.
After Hamilton's homer, Adrian Beltre singled. Nelson Cruz then hit a grounder to Chavez, who chose to try for the force at second, but his throw was late. Fill-in second baseman Jayson Nix's relay to Swisher, the substitute first baseman, was late, putting runners on first and second.
Feldman (6-8) pitched out of trouble in the fourth, fifth and six innings, working around three walks and two hits. In six innings, he allowed seven hits and four walks. He struck out seven.
"I didn't feel I was throwing the ball bad, even when that (third inning) was going on," Feldman said. "I just tried to keep doing what I was doing, and the defense made some plays behind me. They just got one more than us tonight."
Hamilton pulled the Rangers to 3-2 in the sixth, launching a mega-homer way up the bleachers in right. It was his third multihomer game this season.
Ian Kinsler was ejected by plate umpire Vic Carapazza in the eighth inning for arguing balls and strikes. He is 0-for-11 in the series.
Curtis Granderson hit a sacrifice fly after Swisher's double. Then Chavez had a run-scoring single, the first of three hits. The former A's star has been getting the majority of the playing time at third base since A-Rod broke his hand, and he has responded. Chavez has a streak of six straight multihit games to raise his average to .303. A six-time Gold Glove winner whose career has been curtailed by injuries, Chavez is happy with his role.
"With the injuries that I've had, my mindset had to change," Chavez said.
Rangers RHP Koji Uehara (strained right lat muscle) threw 20 pitches in batting practice without problems at Double-A Frisco. The plan is for him to throw 30 in a BP session Saturday. ... Rodriguez (broken left hand) will have another X-ray on Sunday. He said the results will help set the next steps in his rehabilitation. ... Hamilton had a four-homer game this season at Baltimore on May 8. ... Jeter has an 11-game hitting streak. ... Rangers INF Michael Young was given a day off from the starting lineup. He flied out in the seventh as a pinch hitter and played second base in the ninth as Texas lost its DH spot. ... Rain knocked out the TV signal in the press box with one out to go in Seattle ace Felix Hernandez's perfect game.