Ian Desmond and Jonathan Lucroy each had an RBI single for Texas, which has an 8 1/2-game lead in the AL West with five weeks left in the season.
Jason Kipnis opened the scoring with an RBI double in the third against Perez (8-10), who lost at home for the first time since May 13 and dropped to 1-6 with a 6.30 ERA over his past 10 starts.
"If you stay close, we felt we could string a couple hits together", Cleveland manager Terry Francona said. "The last 14 years have been some of the most successful in team history and we look forward to what the future holds for both the Indians and the Rangers".
Cleveland Indians starting pitcher Carlos Carrasco adjusts his cap after giving up a run during the first inning of a baseball game against the Texas Rangers in Arlington, Texas, Saturday, Aug. 27, 2016.
"I don't think there's one magic thing that I can put my finger on", said Kluber, who also won six straight in his Cy Young season.
The Indians stopped a three-game losing streak for the seventh time this season.
"What we always talk about is being consistent and I want to make sure I'm showing that", Holland said. The Rangers challenged and Andrus was ruled safe on a replay review that extended the inning.
Texas designated hitter Carlos Beltran went 0 for 4 with two strikeouts, extending his career-worst slump to 0 for 32. He struck out 13 hitters in a gritty 3-2 come from behind win by the Indians, however, when he pitched Wednesday against the A's, he was shelled for five runs in the second inning in route to a poor loss. In the sixth, a running Gomez made an over-the-shoulder catch on a liner by Mike Napoli. Gomez was sprinting back and reaching over his head when he made the catch.
"He was the hero today", Holland said.
C Chris Gimenez made his second pitching appearance of the season and third of his career, retiring the three batters that he faced in the eighth inning.
Desmond's run-scoring single in the second came on the first pitch after Elvis Andrus had been initially called out on a stolen base.
Except for one big game in Texas, the Cleveland Indians have struggled to score in the past week since leaving home. All of them were singles. He last appeared in a major league game on June 21. Guyer, who came to the Indians at the trading deadline from Tampa Bay, was plunked an AL-high 24 times past year with the Rays.
Indians: Just before the deep fly Gomez caught, Ramirez fouled a pitch off his right leg, just above his knee.
Rangers: There was a short delay in the fourth inning when team photographer Kelly Gavin was struck on the back of the head by a foul ball hit into the photographer's well at the far end of the Rangers dugout.
The Indians return home to start a ten-game homestand by opening a three-game set with the Minnesota Twins (49-81) on Monday. Gavin got the rest of the day off, and team officials said she would be OK.
Rangers RHP Yu Darvish is scheduled to start Monday at home vs. Seattle after hitting his first big-league home run in his previous start last Wednesday in Cincinnati.