James Shields allowed just one run in seven innings, but got a no-decision as the Royals scored just once on a passed ball in the fifth before he left the game.
With the game tied at 1, Alcides Escobar and Eric Hosmer led the 10th inning off with back-to-back singles off Robbie Ross. Billy Butler was then intentionally walked before Mike Moustakas and Lorenzo Cain struck out swinging.
"I liked the matchup with the bases loaded with Moustakas," manager Ned Yost said. "I thought Moose could get on his fastball and I knew that Cain was behind. So I thought one of those guys would pick up the run. When it didn't happen, it was the same thing. I liked the matchup."
Ross then hit Lough on his right wrist with a 2-1 fastball to bring the go-ahead run home. Kottaras bested the pitcher again by lining a ball off the wall in right field, driving in Hosmer and Butler.
"It started out with the cow-milking thing, and you don't ever expect to come into a game in that kind of situation," Kottaras said. "Coming up with that big hit in the 10th, it all runs together. It's a great feeling."
Shields was sharp, allowing just one run on five hits, striking out five and walking one over seven innings. He turned in his ninth quality start in his last 10 outings and lasted seven innings for the sixth time in his last seven starts.
"You've got to tip your hat to him," Rangers first baseman Mitch Moreland said of Shields. "You know you're going to have a tough game when you face him. It's always a grind, because he mixes pitches so well. He throws everything in any count."
Saturday's win marked the sixth straight time the Royals scored three or fewer runs in a game started by Shields. He's 0-4 in his last six starts, despite posting a 2.66 ERA during that stretch.
"I don't care about run support, as long as we win the game," Shields said. "We had a good win. We fought hard. I was able to do my job. That's a good ballclub over there. I was glad we got the win."
Shields was hit by a line drive off the bat of Elvis Andrus in the first inning. The ball hit him in his right arm and hip, but Shields said he was fine. Lough had X-rays on his wrist after being hit in the 10th, which came back negative.
"I just wanted to wear it for the team," Lough said. "It was bad. I couldn't move my finger or anything until 20 minutes later. I started testing it out and a lot of strength came back. I'm more glad we got the win than anything."
Shields retired 10 straight batters after giving up a one-out single to David Murphy in the first inning, but he surrendered three straight hits in the fourth. Adrian Beltre lined a two-out base hit to left and Nelson Cruz blooped another to right, putting runners on the corners for Moreland, who singled up the middle to bring Beltre home and give the Rangers a 1-0 lead.
The Royals responded the next inning, getting a one-out single from Lough, who advanced to third on a single by Elliot Johnson two batters later and scored on a passed ball. With Alex Gordon facing an 0-2 count with two outs in the fifth, Nick Tepesch's pitch in the dirt skipped past catcher A.J. Pierzynski, allowing Lough to tie the game.
The Rangers nearly regained the lead in the fifth when Shields issued a one-out walk to Leonys Martin, who stole second and went to third on an errant throw by catcher Adam Moore. With the infield drawn in, Andrus lined a ball up the middle, but it was snagged by Escobar at shortstop, who threw Andrus out at first and prevented Martin from scoring the go-ahead run.
"He's played great defense for us all year," Yost said. "He's the guy that's anchored our defense at shortstop. He makes spectacular plays. He makes routine plays. You can count on him to make the play if it's anywhere near him."
The victory gets the Royals started off on the right foot in June after going 8-20 in May, recording their fewest wins a month since going 7-19 last July. They've won two of their last three games since losing 12 of their previous 13.