ARLINGTON, Texas -- Delino DeShields Jr. couldn't have picked a better time for his first RBI of the season.

The Texas outfielder drilled a one-out single to left field in the bottom of the 13th inning to lift the Rangers to a 1-0 victory over the Kansas City Royals on Thursday night.

It was the first walk-off win for the Rangers this year, and it ended just the fourth game in Texas franchise history that went to the 13th frame scoreless.

DeShields singled off Travis Wood (0-1) to score Joey Gallo, who led off the inning with a double. Gallo's hit was the first for the Rangers since the fifth inning.

DeShields, who went 1-for-4, collected just his second hit of the year.

"I felt like I was on everything," DeShields said of his 10-pitch at-bat. "If anything, (Wood) probably didn't know what to throw. He probably thought he could get lucky or something -- I don't know.

"I was locked in. I wanted to be the one to come through right there. I kept telling myself there would be a chance. It just happened to be me up there."

As good as the DeShields at-bat was, Texas manager Jeff Banister was just as happy with Gallo's. It gave the Rangers just their sixth opportunity with a runner in scoring position in the game.

"It's a crucial at-bat," Banister said. "We know the power with Joey and the type of hitter he is. He is going to strike out some, but that was a big at-bat for him. ... You could just tell the look in Joe. Every time he steps up to the plate there is a competitiveness in him that he wants to get a job done."

The teams combined for just 10 hits as the Royals played a game that was scoreless through 12 innings for just the sixth time in franchise history -- their first since 1992.

Left-hander Dario Alvarez (1-0), the seventh Texas pitcher, picked up the win with two scoreless innings and three strikeouts.

The Rangers got seven innings of one-hit ball from their bullpen in relief of starter Andrew Cashner. The last Kansas City hit came in the eighth inning, a one-out single from Alex Gordon.

"I think what you saw tonight was two struggling offenses facing off against some pretty darn good pitching on both sides," Kansas City manager Ned Yost said. "We're just trying to make something happen, trying to do more than you're capable of instead of letting it happen. Instead of having good at-bats, you're trying to make it happen and that's not a good recipe for success.

Cashner, a Texas native who was making his first career start at Globe Life Ballpark, walked four but allowed just three hits. The Royals had baserunners against him in five of his six innings but couldn't come up with a big hit. Cashner struck out three.

Kansas City starter Danny Duffy was even better working out of trouble.

The Rangers had runners in scoring position in the second, third and fifth innings but were 0-for-5 with runners in scoring position against Duffy. The left-hander threw 7 1/3 scoreless innings, allowing five hits, striking out five and walking three en route to lowering his ERA to 1.32.

"Both starters did a good job; both bullpens pitched really well," Duffy said. "But somebody's got to come out on the losing end of that. It happens."

Only one batter reached third base in the first nine innings. The Rangers' Jonathan Lucroy doubled off Duffy to open the fifth inning. He advanced to third on a fly ball, but Duffy got Elvis Andrus to fly out to end that threat.

Wood, the fourth Royals pitcher, allowed two hits in 1 1/3 innings.

NOTES: RHP Anthony Bass had his contract purchased by the Rangers and will serve as the long man in the bullpen. To make a roster spot for Bass, the Rangers designated RHP Michael Hauschild for assignment. ... Kansas City 3B Mike Moustakas extended his hitting streak to seven games with a first-inning single. ... The starts by Kansas City LHP Danny Duffy and Texas RHP Andrew Cashner extended both teams' streaks of not having the starter allow more than four runs. The only other team yet to have a starter yield at least five runs is the Los Angeles Dodgers.