ARLINGTON — Prior to Sunday’s series finale against the Twins, Rangers manager Bruce Bochy described his team’s current predicament in perhaps the starkest terms he’s used yet this season.

“You get to this point of the season, and you’re at where we’re at — sure, nothing’s impossible, but you’re realistic,” Bochy said.

After the Rangers’ resilient 6-5 walk-off victory in 10 innings, the distance between what’s possible and what’s realistic seemed closer, more surmountable, though it’s still extremely remote. While they remain mathematically in contention to defend the franchise’s first World Series title, the Rangers are 12 games below .500 and 11 games out of first place in the American League West.

Still, even if Sunday’s win only improved the Rangers’ chances of making the playoffs by a tiny increment, it lifted their spirits. Josh Jung, who had the go-ahead homer in the seventh and singled in the game-winning at-bat in the 10th, said the comeback reminded them that “we’ve still got it in us” offensively.

“We don’t want to give up,” Jung said. “We’re not in the best of situations at the moment, but [let’s] just go out there and compete every night. … Just try to go win every at-bat.”

Jung certainly won his final two at-bats Sunday. His homer pulled the Rangers ahead after they rallied from a 4-0 deficit, and Jung provided walk-off heroics when his 10th-inning infield single led to an error that scored the winning run.

Jung’s homer went a Statcast-projected 420 feet, clanking off the left side of the batter’s eye in center field. The chopper Jung hit on the game’s final pitch traveled all of three feet in the air. But charging third baseman Jose Miranda had to hurry his throw, and Adolis García, who began the inning at second base, bounded home when Miranda’s throw sailed wide of first.

“You get them any way you can take them, I guess,” Jung said.

The Rangers were in danger of being shut out and swept by the Twins with eight outs left. Texas scored only seven runs in the first three games against Minnesota at Globe Life Field — all losses.

“It’s hard to have a tougher series than we had,” Bochy said. “A couple of the previous games got away from us. You’re looking at getting swept. You’re down four runs. The first six innings we created some pretty good opportunities, but couldn’t quite cash in. Then they broke loose.”

In the seventh, the Rangers scored five runs off Jorge Alcala, who had a 0.45 ERA in 19 road games this season before the Rangers got to him in the seventh.

“This was a big one,” Bochy said. “The last thing you want to do is get swept four games at home.”

After leadoff hitter Leody Taveras singled to greet Alcala, the top of the Rangers’ order pounced. Marcus Semien doubled Taveras home and scored on Corey Seager’s double. García followed with a high fly to left-center field, and the ball cleared the wall over Twins left fielder Matt Wallner’s glove, which also sailed over the fence as he attempted to steal the home run. García’s two-run homer, his 21st of the season, tied the game at 4-4.

One out later, Jung put the Rangers ahead with his laser to center.

The Rangers ended up having to overcome one more obstacle Sunday after that rally, however. Closer Kirby Yates was a perfect 21-of-21 in save opportunities this season when he took over to start the ninth — and then Carlos Santana took Yates deep with a leadoff, game-tying homer.

Texas’ comeback and subsequent walk-off spared Yates and Texas starter Tyler Mahle, whom the Twins knocked around for six hits and four earned runs in only three innings. Mahle notched a strikeout to start the game, but surrendered a three-run homer to Ryan Jeffers later in the first inning and an RBI single to Jeffers in the third.

Though the starter and the closer faltered, middle reliever Gerson Garabito kept the Rangers in the game with four no-hit innings after he replaced Mahle.

“He saved us,” Bochy said. “Terrific job, the bullpen has been used quite a bit. He was the freshest, so to go out there and keep putting up zeros, he gave us a chance to come back. That’s his win.”