"Hopefully, we can play more games like we did tonight," he said.
Dickey (11-12) gave up two hits in seven innings and the Blue Jays won their third straight as they try to stay in the AL wild-card race.
"We hope we heat up," manager John Gibbons said. "August was a lean stretch for us, but that's over with now. We don't want to think about that."
Jose Bautista's streak of homering in five straight games ended, but he had two singles and an RBI for Toronto.
Dickey gave up two runs, struck out six and walked three.
"From a movement standpoint, I had a really good knuckleball tonight, and it was tough to control it," said Dickey, who pitched at least six innings for the 13th time in 14 starts.
"I hit a couple batters, balls were really tailing off late in the zone, which speaks to how many balls they put into play hard -- not many, which is good. Outside of that one inning, I felt like I was right on point," he said.
The Rays got both of their hits and runs in the second.
Reyes, who singled and scored in the third, had his 13th multiple-hit game in his last 29 games.
Hellickson gave up five runs on eight hits in 3 1/3 innings, the shortest of his nine starts since coming back from January elbow surgery.
"I think it was a matter of locating the ball to some spots that were better suited for the Blue Jays than us," Rays manager Joe Maddon said.
A win on Wednesday or Thursday night would give the Blue Jays their first series victory at Tropicana Field since April 6-8, 2007.
"I don't think anybody's throwing in the towel," Dickey said. "Who knows what a good September might do for us? If we can finish strong and worry about us, not other people, you never know what can happen."
Blue Jays: INF Brett Lawrie (oblique) was transferred from the 15- to 60-day disabled list, which ends his regular season. ... RHP Brandon Morrow (finger) and 1B Dan Johnson (hamstring) were activated from the disabled list. ... LHP Brett Cecil was unavailable due to some minor stiffness.
Rays: CF Desmond Jennings (sore left knee) was out of the lineup for the fifth straight game.
Rays RHP Chris Archer (8-7) and Blue Jays RHP Marcus Stroman (8-5) are Wednesday night's scheduled starters. Archer is coming off a loss to Boston Friday where he gave up a season-high eight runs in four innings.
Former Blue Jays pitcher and one-time Rays bat boy Jesse Litsch threw the ceremonial first pitch. The St. Petersburg native, who announced his retirement last month, went 27-27 over parts of five seasons with Toronto.