Snell won his ninth straight start in Tampa Bay's 5-2 victory over Toronto on Sunday and boosted his record to 21-5.
''I think I'll be telling my grandkids that I played behind him,'' Rays outfielder Kevin Kiermaier said.
Tampa Bay remained 7 1/2 games behind Oakland for the AL's second wild card and would be eliminated with one more loss or win by the Athletics.
Snell struck out 11 in 6 2/3 shutout innings, broke the Rays season record for wins set by David Price in 2012 and lowered his ERA to 1.90, the best in the AL.
''Everything was good today,'' Snell said. ''I felt really good, felt in synch with my body.''
Snell has not lost since July 12 and is 9-0 with a 1.03 ERA starting his streak with a win at Toronto on Aug. 10. He matched the Tampa Bay record for consecutive winning decisions set by Matt Moore from Sept. 29, 2012, to May 19, 2013.
With 175 2/3 innings, Snell trails fellow AL Cy Young candidates such as Houston's Justin Verlander and Cleveland's Corey Kluber, both of whom have eclipsed 200. That doesn't matter to Rays manager Kevin Cash.
''I think he's pretty much cemented his case that he belongs, not just in the conversation but right at the top of the list,'' Cash said. ''He's been dominant now for a couple of months.''
C.J. Cron and Brandon Lowe homered for the Rays, who are 16-5 in September and a major league-best 25-7 since Aug. 19.
Tommy Pham reached base three times and scored twice as the Rays improved to 11-5 against Toronto thus year. He walked in the first, singled and scored on Joey Wendle's two-out double in the fourth, then walked and scored on Cron's two-out double in the sixth.
Cron connected off Joe Biagini in the eighth, his 28th. Jose Fernandez walked Wendle, and Lowe followed with a two-run drive.
Snell allowed three hits and walked two. Four relievers followed, including Sergio Romo, who pitched around a pair of singles in the ninth for his 23rd save in 31 chances.
Blue Jays rookie left-hander Ryan Borucki (4-5) allowed two runs and three hits in seven innings.
''I was just trying to keep this thing as close as we could,'' Borucki said.
END OF THE ROAD
Tampa Bay finished the road portion of its schedule at 39-42, their best record away from home since going 41-40 in 2014.
LEFT IN THE DUST
Toronto is 15-36 against left-handed starters.
Rays: Kiermaier stayed in the game after crashing hard into the scoreboard making a leaping catch on Randal Grichuk to end the fourth, but was replaced by Austin Meadows in the eighth. Kiermaier said his left shoulder was immediately sore following the play, and the pain got worse when he batted in the seventh. ''You don't want to push anything like that,'' Kiermaier said. The two-time Gold Glove winner also made a great catch on Jonathan Davis' sinking line drive for the final out of the third, stranding a runner at first.
Rays: RHP Diego Castillo (3-2 3.25) will open for Tampa Bay as the Rays return home Monday to begin a four-game series against the New York Yankees. RHP Luis Severino (18-8, 3.38) is expected to start for the visitors.
Blue Jays: RHP Marco Estrada (7-13, 5.57) starts the opener of the three game series against visiting Houston. Estrada is 0-4 with a 9.43 ERA in his past five starts. LHP Dallas Keuchel (11-11, 3.71) starts for the Astros.
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