Snell took a no-hit bid into the seventh inning and got his major league-leading 19th win, leading the Rays over the Cleveland Indians 3-1 on Wednesday.
"I know that we're winning and that's the most important thing," Snell said. "That's what I'm focused on, that's what we're focused on. All the individual stuff I'll look at later."
Snell (19-5) lost his bid when Jose Ramirez led off the seventh with his 38th homer. Snell won his team-record seventh straight start, striking out nine and walking two in seven innings. He has allowed two earned runs or fewer in 16 consecutive home starts.
The Rays are 8 1/2 games behind Oakland for the second AL wild card with 17 left. The Athletics routed Baltimore on Wednesday night and open a three-game series at Tampa Bay on Friday night.
Snell's ERA dropped to 2.03, second in the AL behind Boston's Chris Sale at 1.96. Snell's 1.24 ERA at home is best in the majors.
"He's got the whole package," Indians manager Terry Francona said. "He's got velocity, breaking ball, changeup, and seeing how much he's improved from one year to the next, that's pretty special stuff."
Cleveland's magic number to clinch a third consecutive AL Central title remained at three.
Ji-Man Choi hit a two-run homer in the first off Carlos Carrasco (16-9), then took a well-inside pitch from Carrasco in the sixth and briefly stared at the mound. Choi hit a winning homer off Brad Hand in the ninth inning on Monday night.
"Every at-bat I can hit a home run you feel great, especially today helping to contribute to a win for Snell," Choi said through a translator.
Cleveland's Edwin Encarnacion stared and shook his head after a high and inside pitch from Snell in the fourth.
"It was nothing," Encarnacion said. "No hard feelings. He tried to go inside. No problem."
Carrasco (16-9) gave up three runs and six hits in seven innings.
Josh Donaldson, acquired by Cleveland from Toronto on Aug. 31, hit into a double play as a pinch-hitter in the eighth. He went 0 for 4 Tuesday in his Cleveland debut, his first big league game since May 28.
Tommy Pham extended his career-best hitting streak to 16 games with a two-out infield single in the first and scored on Choi's drive to center field.
Indians: Donaldson is to start at third base on Friday.
Rays: CF Kevin Kiermaier didn't provide details for what the team called a "general illness" that kept him out the lineup the previous two games. "Time to rest really helped," said Kiermaier, who had a fourth-inning sacrifice fly and tripled during the sixth.
Ramirez's homer was his first since Aug. 17, ending an 88 at-bat drought. ... Tampa Bay OF Mallex Smith stole two bases and has 33 overall. ... The game was played in 2 hours, 20 minutes.
Indians: RHP Mike Tomlin (1-5) is to face Detroit LHP Matthew Boyd (9-12) on Friday night.
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The Los Angeles Dodgers ruined Arizona's season.
Two right-handers who hope to remain part of the starting rotation next season will go head-to-head when the Los Angeles Angels host the Texas Rangers on Monday in the opener of a three-game series at Angel Stadium.
Two teams playing out the string of losing seasons will open a three-game series Monday night when the San Diego Padres visit the San Francisco Giants.
Minutes after the St. Louis Cardinals coughed up a lead and lost on July 14 to the Cincinnati Reds to drop to 47-46, manager Mike Matheny said they had a good run in them.
The Oakland Athletics will travel to Seattle with a little extra luggage.
The Colorado Rockies have a short, simple agenda as they begin a four-game series Monday with the slumping Philadelphia Phillies.