"Of course you're going to look at the offensive outburst, but Wade Davis really pitched well today. He permitted that to happen," Rays manager Joe Maddon said. "I thought he had really good stuff. He had a good look about him. That set the whole thing up."
Kelly Shoppach also homered as the AL wild-card leaders won for the third time in four games.
Davis (12-9) improved to 3-0 with a 3.24 ERA in four starts since a stint on the 15-day disabled list caused by a strained right shoulder.
"He's come off the injury and I believe he's throwing the ball better than I've ever seen," Maddon said. "I'm talking about last year in September, and I'm talking at any point during this season. I'm talking velocity, depth on breaking ball, demeanor on the mound, awareness. All those things are getting better and that's why he's pitched so well."
Tampa Bay scored six runs in the first inning of Friday's series opener but blew an 8-1 lead before winning 9-8.
This time, Davis made sure there'd be no Toronto comeback. The right-hander, who leads AL rookies in wins, allowed one run and seven hits in seven innings, struck out six and walked three.
"I felt good and I felt under control," Davis said. "My fastball was good, my command was good early and I established it. To get a big lead like that it makes things a little easier."
Not surprisingly, Davis said his confidence is soaring.
"It's definitely higher than it's ever been," he said. "Not in an arrogant way at all, just as far as being able to repeat my delivery. If you can repeat your delivery, you're going to be able to make pitches and I've been doing that pretty good lately."
Hawpe's homer was his second with the Rays, who signed him to a minor league contract on Aug. 27. He went 2 for 5 and scored twice.
Shoppach hit a two-run homer off Rommie Lewis in the eighth.
Lyle Overbay replied with a solo shot for the Blue Jays, who have connected in 13 straight games, matching a season high. Toronto also went deep in 13 consecutive games from July 3-20.
Toronto leads the majors with 223 home runs, including a big league-high 127 at home.
Ricky Romero (12-9) allowed six runs, three hits and three walks in four innings, striking out seven. He breezed through the first three innings, allowing just a single to Evan Longoria, but gave up six runs in the fourth.
Jason Bartlett drew a leadoff walk, Romero hit Carl Crawford with a pitch and Ben Zobrist hit a two-run double with one out. Romero loaded the bases with walks to Carlos Pena and Sean Rodriguez, and Hawpe homered to right for his third career slam and first this season.
"Romero was really good in the beginning and then all of a sudden we jumped on him and had that big inning," Maddon said. "Of course, Brad's grand slam really put us over the top. He had some really good at bats today."
Romero had no explanation for his sudden lapse in command.
"It's one of those mysterious things that happens in baseball, you just lose it all of a sudden," Romero said. "I don't know how to explain it. I think that for the first time all year I got frustrated at myself for not throwing strikes."
Overbay homered off Davis in the fourth, but the Rays made it to 7-1 when Zobrist and Pena hit back-to-back doubles off Brad Mills in the fifth.
Toronto loaded the bases in the bottom half but, after a visit by pitching coach Jim Hickey, Davis struck out Overbay to end the threat.
NOTES: Carl Crawford tripled and is 15 for 32 with nine extra base hits, including four triples, in the past eight games. ... Toronto 3B Edwin Encarnacion, out since Aug. 29 with a sore left wrist, rejoined the team Saturday and is eligible to come off the 15-day DL Monday. ... The Rays are a major league-best 33-17 when facing a left-handed starter. ... Rays OF Desmond Jennings got his first major league hit, a pinch-double in the eighth. ... Tampa Bay is a major league-best 43-29 on the road.