Hamels allowed four singles over seven innings, Delino DeShields doubled home two runs and the Rangers beat the Royals 4-1 on Tuesday night to extend their winning streak to a season-high four games.
The Royals have lost eight straight, matching their season high, and 14 of 15. They own a major league-worst 10-28 home record, and their 22-51 overall mark is the worst in franchise history after 73 games.
Hamels (4-6) picked up his first win since May 22. The run off him in the fifth was unearned, and he has yet to allow an earned run in 20 innings over three starts at Kauffman Stadium.
''To be able to get the runs that we did in the second and third, that was huge,'' Hamels said. ''Just to kind of let you settle down and I felt good from there.''
Keone Kela pitched a spotless ninth for his 17th save in as many chances.
DeShields' second-inning double scored Isiah Kiner-Falefa and Robinson Chirinos.
Kiner-Falefa, who had three hits and walked, doubled home Adrian Beltre in the third. Jurickson Profar scored the second run of the inning after third baseman Mike Moustakas' fielding error to make it 4-0.
''Early in the day he (Kiner-Falefa) wasn't initially in the lineup, but it's a testament to what he does every single day, the professionalism he shows up with, even as a young player, a rookie player, he comes prepared,'' Rangers manager Jeff Banister said. ''He was one of the first players at the ballpark ready to play and he came up big for us tonight with the doubles.''
Royals starter Jason Hammel (2-8) was removed after 5 2/3 innings, allowing four runs on nine hits and four walks. Hammel is 0-6 in nine home starts since an Aug. 20 victory over Cleveland.
''Four walks and two of them came around to score,'' Hammel said. ''That's the thing that will irk me as I'm trying to sleep. I had trouble gripping the ball the first few innings. I was just sweating like a dog. It's an excuse. It's something I've dealt with my whole career. I sweat a lot.''
Rosell Herrera's two-out double in the fifth scored Alex Gordon with the Kansas City run.
Whit Merrifield led off the Royals' first with a walk, took second on a wild pitch and stole third with none out, but did not score. Salvador Perez grounded into his 12th double play after Moustakas walked to end the inning.
''We've hit into our 73rd double play of the year, something crazy,'' Royals manager Ned Yost said. ''It just boggles your mind that that has happened so many times.''
Gordon picked up his seventh outfield assist of the season, throwing out Elvis Andrus trying to score from second on Profar's ninth-inning single.
GAME TWO TIDBITS
The Rangers have more than half of their 31 victories in the second games of series. They are 16-8 in Game 2s.
JUST LIKE DAD
Adalberto Mondesi doubled off Rangers RHP Bartolo Colon on Monday. His father Raul Mondesi went 2 for 11 off Colon. The Mondesi family is the fourth father-son combo to each record a plate appearance against the 45-year-old pitcher.
Rangers: LHP Yohander Mendez was optioned to Triple-A Round Rock after violating team rules. RHP Austin Bibens-Dirkx was recalled from the same club. ... Texas traded RHP Deck McGuire to the Los Angeles Angels for cash or a player to be named.
Royals: RHP Heath Fillmyer was recalled from Triple-A Omaha, where he was 4-5 with a 5.75 ERA in 13 starts. He will be used in relief.
Royals: 1B Lucas Duda (right foot plantar fasciitis) went 2 for 5 with a three-run homer and a double in Omaha's 9-2 victory Tuesday in Reno in his second minor league rehab game. OF Jorge Bonifacio, who is suspended for the first 80 games for violating the MLB's drug policy, is hitting .448 in seven games with Omaha.
Rangers: Bibens-Dirkx (0-1, 6.55) will start the series finale. He went 2-3 with a 4.47 ERA in 11 starts with Round Rock.
Royals: RHP Jakob Junis (5-7, 4.43) has lost his past four decisions. He has never faced the Rangers.
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