"It's more about the ascension of the Rays right now," Tampa Bay manager Joe Maddon said. "Obviously, they're struggling a bit, and that happens. But from our perspective, it's more important what we do. It's fortuitous that they've had a hard time, but I love the fact that we're taking care of business."
Nine games back of the Red Sox heading into play on Sept. 4, Tampa Bay would move into a tie for the wild-card lead if the Yankees completed a sweep of Boston in their day-night doubleheader.
"The more pressure you put on yourself, the tougher it is to play baseball, which is probably what the Red Sox are doing right now," Davis said. "There's probably a lot of pressure on them. They're playing tense and they're not playing their game. As long as we can stay relaxed and understand our position, we can just keep it going."
No major league team has overcome a nine-game deficit in September to claim a postseason berth. The closest was the 1964 World Series champion St. Louis Cardinals, who trailed the Philadelphia Phillies by 8˝ games on Sept. 3.
Tampa Bay closes at home against the Yankees, while the Red Sox play at Baltimore.
"I know we have a tough team coming in, and we really have to play well," Tampa Bay's Johnny Damon said. "It'll be a tough go, but I think we're feeling good about ourselves and fortunately for us, there's no off-day."
Davis (11-10) allowed two runs and three hits in eight innings, and Joel Peralta finished for his sixth save in eight chances. The Rays have won 27 games in a row when scoring five runs or more.
Toronto's Jose Bautista, the major league leader with 43 homers, bruised a spot just below his left knee on Zobrist's first-inning homer, hitting the right-field fence hard while attempting to make a catch. Mark Teahen hit for Bautista in the sixth inning.
"It's sore right now," Bautista said. "It started getting more sore and stiff to run. It was hurting when I was running."
Blue Jays manager John Farrell doesn't expect Bautista to play in Monday night's game at the Chicago White Sox. The slugger hasn't ruled himself out from playing again before the regular season ends Wednesday.
"We feel like we dodged a bullet," Farrell said. "It could have been something much more severe. There's a little bit of a gap in that padding out there, and there's a little bit of exposed metal and that was the impact."
Upton homered with one out, and Zobrist hit an inside-the-park homer to right with two outs, also off Brett Cecil (4-11).
David Cooper had an RBI double in the second, but Longoria's two-run homer made it 4-1 in the third. He has driven in 82 runs over his last 95 games.
After Toronto's Dewayne Wise had a solo homer in the fifth, Shoppach hit a sixth-inning shot.
Cecil gave up four runs and five hits in 3 1/3 innings. He is 0-7 with a 5.16 ERA in his last 10 starts.
RHP James Shields (15-12), who leads the majors with 11 complete games this season, will start Monday night's game against the Yankees. He will be followed in the series by Jeremy Hellickson (13-10) and David Price (12-13). "Everything is lined up properly right now," Maddon said. "Let's just go out and play, and see what happens." ... Blue Jays CF Colby Rasmus was a late scratch due to fulike symptoms. ... 1B Adam Lind, who left the team Friday for the birth of his child, missed his third straight game. ... Farrell will miss Monday night's game with the White Sox to be with his 20-year old son Luke, who is having scheduled surgery. ... Zobrist has four homers in his last eight games after going 39 games without one. ... Farrell said it's becoming more unlikely that SS Yunel Escobar (left elbow) will play again this season. ... Toronto RHP Dustin McGowan (0-1) and Chicago RHP Dylan Axelrod (0-0) will pitch Monday's series opener.