Garcia had three hits, including his seventh home run, and three RBIs. Texas is 3-0 in extra innings this season and has scored 10 of their 11 runs in the series in the eighth inning or later.
''Innings one through nine, he's already got a game plan going into the game, just kind of go through a routine,'' Garcia said through an interpreter. ''That situation that came up, he just kind of was ready for it. There's no really any type of pressure. He continued to go to his plan.''
Kyle Gibson, making his first start against his former team, gave up three runs and three hits with eight strikeouts.
Joely Rodriguez (1-1) struck out two in a perfect ninth, and Ian Kennedy gave up a leadoff single before getting a strikeout and game-ending double-play grounder for his eighth save in as many chances.
''Adolis, for some reason, has a flair for the dramatic,'' Rangers manager Chris Woodward said. ''Seems to get a big hit every time we need it. Big home run when we need it, not surprising, I guess. That's just speaks to this team and the energy we have right now, it's pretty special.''
Brandon Waddell (0-1) gave up all three runs in the 10th for Minnesota after Taylor Rogers allowed Willie Calhoun's leadoff homer and Isiah Kiner-Falefa's sacrifice fly in the ninth, which followed third baseman Josh Donaldson's fielding error on Charlie Culberson's grounder.
Shortstop Andrelton Simmons managed to track down Kiner-Falefa's fly but with Simmons' back turned to the plate, Culberson raced home.
The Twins are 0-6 in extra innings this season.
''Any loss like this is tough, but when you have a bunch of in the first one month to start the year, it's especially hard,'' Minnesota manager Rocco Baldelli said. ''We've played a lot of games where we're playing winning baseball, we're going into the last inning or two ahead, sometimes well ahead and we haven't been able to win those ballgames. We have to win those ballgames. We just have to.''
Byron Buxton hit a two-run homer in the first inning for the Twins. Willians Astudillo added a solo home run, but Minnesota only had only four hits.
''I think we've got to score more runs, obviously,'' Twins catcher Mitch Garver said. ''I think our offense needs to pick it up a little bit. Gibby did throw really well tonight. Just shake it off. We'll get them tomorrow.''
Gibson, in his second season with Texas, spent seven years pitching for the Twins after being a first-round draft pick in 2009. Tuesday marked his 95th career start at Target Field, the most of any player.
Since giving up five runs in just 1/3 of an inning on Opening Day, Gibson has allowed six runs total over his last six starts, spanning 41 innings.
''I think they were really patient in the first inning and I think that caught me off guard a little bit,'' Gibson said. ''The pitch to Buxton was maybe one of my worst sliders of the night. I think that just comes from being a little more amped up and a little more excited. You end up leaving the ball up a little bit there when you're trying to go down and in.''
Rangers: INF Brock Holt was placed on the 10-day IL with a right hamstring strain. INF Andy Ibanez's contract was selected from Triple-A Round Rock, and he made his major league debut with a pinch-single in the ninth. . RHP Kohei Arihara played catch Tuesday and reported no pain in his right middle finger, but he will not start on his regularly scheduled day on Wednesday. Arihara will throw a bullpen session on Thursday and would tentatively start on Saturday if he suffers no discomfort. . C Sam Huff (right knee surgery) was moved from the 10-day to the 60-day IL.
Twins: IF/OF Luis Arraez was placed on the seven-day IL with concussion-like symptoms. Arraez sustained the injury in a home-plate collision in Monday's game. To replace Arraez, Minnesota recalled INF Nick Gordon from Triple-A St. Paul. . RHP Michael Pineda won't start in his scheduled slot on Wednesday as he deals with a wrist injury. Pineda could possibly start on Thursday with the rest of the rotation pushed back a day. . Rookie Alex Kirilloff was held out of Tuesday's lineup with a sore wrist. Baldelli said Kirilloff will see a hand and wrist specialist on Wednesday.
Minnesota will recall LHP Lewis Thorpe (0-0, 3.60 ERA) from Triple-A to start Wednesday's game. Thorpe pitched in two games earlier this season for the Twins. Texas will counter with LHP Hyeon-Jong Yang (0-0, 2.08). Yang will be making his first major league start after he allowed two runs in two relief appearances over 8 2/3 innings. Yang, 33, played 14 seasons in South Korea before signing with the Rangers in February.
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