The Rangers even did it without Aroldis Chapman, the Yankees' closer who is now the latest marquee player rumored to be on the trade block as the Aug. 1 non-waiver Deadline approaches. The Rangers have had their name attached to Chapman -- as they have with every pitcher -- but on a hot afternoon at Kauffman Stadium, they were able to rely on the usual suspects, as Sam Dyson closed this one out for his 20th save.
"It was awesome," Dyson said. "Obviously it was nice to see. We all expect our bullpen to be able to do that. It's not going to turn out like this all the time, but we have a good bullpen. We'll just continue to grind it out and see where it all is in the end."
The one variation on the standard bullpen plan employed by the Rangers on Sunday was left-hander Alex Claudio being used in a high-leverage situation rather than the usual lopsided affair.
Griffin went five innings, allowing just one run, before Claudio came on in the sixth inning and faced the big bats in the middle of the Royals' order: Eric Hosmer, Kendrys Morales and Alex Gordon. Hosmer and Gordon are left-handed hitters while Morales is a switch-hitter.
"Coming into the series, looking at the numbers, we felt comfortable with Claudio against those set of hitters if we needed to go that way," Rangers manager Jeff Banister said.
Hosmer flied out to right to start the inning and Morales doubled into the left-field corner. Gordon followed with a grounder back to the mound and Claudio was able to catch Morales off second base in a rundown for the second out. Paulo Orlando grounded out to end the inning.
"I was just attacking the zone, throwing strikes and not getting behind in the count," Claudio said. "Those guys are good. It was a big situation, and I was happy my manager gave me a chance to help out in those situations."
Delino DeShields put Claudio in a position to get the win with a seventh-inning home run that put the Rangers in the lead. Texas just needed nine outs, and Banister brought in the power arms.
Keone Kela retired the side in order in the seventh, striking out two, and Jake Diekman did the same in the eighth with one strikeout. Dyson wasn't so clean in the ninth. He gave up a leadoff base hit to Morales and a two-out single to Salvador Perez.
That put runners on first and second, but Dyson ended it by getting Christian Colon to hit a roller in front of the plate. Catcher Robinson Chirinos pounced on it and fired to first for the final out.
"That's a good baseball game right there," DeShields said. "You can't ask for anything more. We had a couple opportunities to really bust it open. But we got the lead and the pitchers held it, and Dyson came in and got the save."
The victory brought the Rangers nine-game road trip to an end. They were only 3-6 on the trip, but they return to Arlington on Monday night with a 2 1/2-game lead over the Astros in the American League West.
"It was a tough road trip, especially here where the heat was unbelievable," Elvis Andrus said. "We're glad to be able to win the series, that's what matters. Now we can go home and play in front of our own crowd."
T.R. Sullivan has covered the Rangers since 1989, and for MLB.com since 2006. Follow him on Twitter @Sullivan_Ranger and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.