The Rangers are 10-3 since having their division lead cut down to three games on July 31. After Oakland lost Sunday, the Rangers now top the AL West by 6 1/2 games.
"I just hope we can maintain what we have been doing," Hamilton said.
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Hamilton is a big reason for Texas' surge. He was mired in a lengthy slump when manager Ron Washington gave him a mental day off on July 28. The slugger was then briefly dropped to the fifth spot in the lineup for the first time in two years.
The 2010 AL MVP has responded since then, hitting three home runs with 15 RBIs in 11 games. The Rangers have gone 8-3 in that span.
Hamilton had a two-run drive in the first inning, taking the major league lead and matching his career high. He added an RBI single to give him 99 RBIs, which is also tops in baseball.
Darvish (12-8) allowed six hits and walked five to snap a personal two-game losing streak and help the Rangers take two of three from the Tigers.
After starting the season 10-4, Darvish went 1-4 with a 7.04 ERA in six starts before Sunday.
"He was the king and he acted like he was the king on the mound," Washington said.
Miguel Cabrera had a two-run double as the Tigers slipped two games behind the Chicago White Sox in the AL Central.
Rick Porcello (9-7) gave up nine hits and six runs. The right-hander is 2-3 lifetime against the Rangers with a 7.83 ERA in five starts.
The Tigers committed three errors and threw three wild pitches. Detroit's offense was held to 11 hits in losing the last two games.
"It was ugly, really ugly," Detroit manager Jim Leyland said. Darvish improved to 3-0 against the Tigers this season as he avoided his first three-game losing streak.
With temperatures over 100 degrees, Darvish threw 120 pitches.
"I felt like I was stronger in the end," Darvish said through an interpreter. "So the heat didn't affect me."
The Rangers next travel to New York for a four-game set against the Yankees in a matchup of the two top teams in the AL.
"We always enjoy playing in New York," Hamilton said. "But it's just another series."
Hamilton's 419-foot long ball -- his third homer in four games -- easily cleared the fence in center and gave Texas a 2-0 lead. He equaled his career high in home runs, a mark he established in 2008 and 2010.
Texas scored three runs in the third with the help of two Detroit errors.
Kinsler's RBI double made it 3-0, and he came home when Porcello made an errant throw toward third after fielding a hopper.
Hamilton capped the inning with an RBI single to right that Brennan Boesch booted, allowing Hamilton to advance to third.
Texas increased its advantage to 6-0 on Kinsler's sacrifice fly in the fourth before the Tigers touched up Darvish.
"I wanted to get back to my old form," Darvish said. "This was a big step."
Omar Infante's RBI double in the fifth snapped a 12-inning scoreless slump, and Cabrera's two-run double off Darvish gave him 98 RBIs and brought the Tigers to 6-3.
The Rangers scored twice in the seventh thanks to three wild pitches and an error.
- Texas infielder Alberto Gonzalez cleared waivers and accepted an assignment to Triple-A Round Rock on Sunday. The Rangers had designated Gonzalez for assignment Friday.
- Detroit LHP Daniel Schlereth (left shoulder tendinitis) pitched a scoreless inning in a rehab appearance for Class-A Lakeland on Saturday.
- Rangers RHP Koji Uehara (right lat strain) threw a bullpen session Sunday. He is scheduled to pitch batting practice in Double-A Frisco on Wednesday.