In his second at-bat of the nightcap, Suzuki hit a slow roller to shortstop Elvis Andrus, beating his throw for No. 200 and driving in a run to make it 2-0.
Suzuki, who went 1-for-5 in the second game, received a standing ovation from the sparse crowd, stepping off first base and doffing his batting helmet to thank the fans.
He had been tied with Willie Keeler, who had eight consecutive 200-hit seasons from 1894-1901.
In the opener, Suzuki doubled in four at-bats, but Texas rookie Tommy Hunter threw a six-hitter for his first complete game and the Rangers hit three homers in their 7-2 victory.
Hernandez (15-5) struck out five and walked one in the nightcap, retiring 10 in a row from the third through the sixth. He's given up one run or less and lasted at least seven innings in 15 of his 30 starts this season.
Adrian Beltre's two-run homer in the fifth inning of the nightcap extended Seattle's lead to 5-0.
Texas was playing its third doubleheader this month due to rainouts. The Rangers swept the first two.
Rain that pelted the area for the past four days caused the opener to begin 4 hours, 31 minutes after the originally scheduled start time of 12:35 p.m. It was a makeup of Friday night's rainout.
The Rangers fell four games behind Boston for the AL wild card. The Red Sox swept a doubleheader from slumping Tampa Bay at Fenway Park.
Seattle got an RBI double from Jose Lopez off rookie Derek Holland (7-11) in the first inning of the second game, and Jack Wilson's run-scoring single in the fourth made it 3-0.
Holland lost his fourth straight start, giving up five runs and eight hits in six innings.
Hunter fared better than his fellow Rangers rookie, getting loose before his start by playing cards, pingpong and video games, including Ken Griffey Jr. Slugfest.
Griffey went 0-for-4 in the first game.
Hunter (8-3) struck out three and walked one in his 15th big league start, polishing off his first professional complete game with 102 pitches.
Chris Davis, David Murphy and Nelson Cruz connected for the Rangers in the opener.
Seattle rookie Doug Fister (2-2) gave up five runs and 10 hits in 4 2/3 innings of the opener.
The Rangers are still missing two All-Stars: outfielder Josh Hamilton and third baseman Michael Young. Hamilton has missed the last eight games with a pinched nerve in his back and Young has sat out the past nine with a strained left hamstring.
Both could return for this weekend's series against the AL West-leading Los Angeles Angels.
Notes
The Mariners had their ninth shutout of the season. Mark Lowe, who played in college for Texas-Arlington, pitched the eighth and David Aardsma pitched the ninth to finish off the M's ninth shutout of the season. … Texas rookie Julio Borbon had three hits in the second game. … The Rangers were shut out for the second time in their last seven games. … The Rangers hadn't started rookie pitchers in a doubleheader in nearly 31 years. Steve Comer and Danny Darwin got the starts against Seattle on Sept. 24, 1978 in Arlington. … Andrus hit safely in both games, extending his hitting streak to 15 games, longest by a rookie in the majors this season. He also tied George Wright (1982) and Jerry Browne (1987) for the rookie club record.