Darvish (15-9) struck out nine in seven innings, often complementing his mid-90s fastball with a breaking pitch about 30 mph slower.
Ian Kinsler hit his sixth leadoff homer this year for Texas, a ball initially ruled a double before umpires looked at the replay and correctly reversed that call.
There was no question about Hamilton's long drive in the third off Hisashi Iwakuma (6-5), like Darvish a former Pacific League MVP in Japan and now a rookie in the major leagues.
With 205 strikeouts, Darvish is the first rookie over 200 since Daisuke Matsuzaka struck out 201 batters for Boston in 2007. He is the 16th rookie, sixth in the American League, with 200 strikeouts.
While only the eighth time two Japanese starters to pitch against other in the majors, Darvish and Iwakuma faced each other six times in Japan. Darvish last season threw a complete game for Hokkaido in a 2-0 win over Rakuten and Iwakuma, who worked 8 2-3 innings in that game.
Darvish retired 12 of the last 13 Mariners he faced, with seven of his strikeouts in that span. He allowed only two hits and walked two while throwing 79 of his 110 pitches for strikes.
It was Darvish's third consecutive start of at least seven innings while allowing three hits or less. The only other Rangers pitcher to ever do that was Hall of Famer Nolan Ryan, now the team president sitting in the front row. He did it in 1990.
After Carlos Peguero led off the fifth with a strikeout, Darvish's fourth of the game and 200th of the season, the Japanese star quickly added to that total. Trayvon Robinson took a called third strike and Munenori Kawasaki struck out swinging, missing a 94 mph pitch right after taking a 62 mph curve over the plate.
Michael Saunders led off the Seattle fourth with a 12-pitch walk. Kyle Seager followed with a double and Saunders scored on a sacrifice fly by Jesus Montero. In their previous game at Rangers Ballpark on May 30, the Mariners won 21-8.
Saunders led off the ninth with his 15th homer.
Iwakuma struck out four with one walk in 5 1-3 innings. He gave up seven hits, and the only runs he allowed were on the two solo homers.
Kinsler's ball skipped over the top of the left-center field wall and ricocheted off a chair in the Mariners bullpen and back onto the field. It didn't take umpires long to reverse their call after leaving the field momentarily.
Hamilton was back in the lineup after getting an injection in his sore left knee and missing a game. He pulled a ball into the second deck of seats in right field in the third.
After Elvis Andrus led off the eighth with a double, he scored on a double by Hamilton. Andrus had a bases-loaded triple to cap the seven-run eighth off four Seattle pitchers that made it 9-1.
Hamilton's 42 homers and 123 RBIs lead the majors.
NOTES: Darvish is 4-1 with a 2.32 ERA his last six starts. ... The tarp wasn't taken off the field until an hour before the game, and there was still a light rain falling when the game started on time. It stopped about midway through the game. ... Seattle's defense turned consecutive inning-ending double plays. After David Murphy's liner ended the sixth, Kinsler's attempted bunt in the seventh was caught in the air by pitcher Josh Kinney and turned into a double play.