And the rest of the team also stepped up, with Brett Lawrie and Edwin Encarnacion combining to drive in four runs in a 7-1 victory over the Boston Red Sox.
Toronto (12-13) leaves for an eight-game road trip, which starts Tuesday in Kansas City, having washed away the taste of a sour four-game losing streak at home.
The Jays, who had given up 36 runs on 47 hits and 22 walks during the four-game slide, badly needed a change of direction. Dickey said a talk by manager John Gibbons after Saturday's 7-6 loss, when a Jays comeback fell just short, had done the trick.
"He was just so encouraging," said Dickey, who got the win on his first major-league bobblehead giveaway day. "I think everybody left the clubhouse feeling at ease about who we are as a team. So we just needed to come out today and be ourselves. And we were able to do that.
"We fought hard. Guys were getting dirty, diving for balls, taking the extra base. I was able to throw strikes and we had a great team win today."
Said Gibbons: "It was a much-needed win, I will definitely say."
On a weekend where racism in sports made headlines thanks to Los Angeles Clippers owner Donald Sterling, the Jays made Major League Baseball history with a record six Dominicans in the starting lineup: Encarnacion, Jose Reyes, Melky Cabrera, Jose Bautista, Juan Francisco and Moises Sierra.
The Dominicans signed the lineup card, which Bautista said was going to be sent to the Dominican Museum of Baseball.
"It was an honour to be part of that today," said Reyes.
An announced sellout of 45,260 at the Rogers Centre saw Dickey outduel Jon Lester with Lawrie providing the early offence before the Jays put the game away with two runs in the seventh and three in the eighth.
Lawrie, who entered the game hitting .165 but leading the team in RBIs, drove in two runs with a homer and double to increase his RBI total to 20.
Dickey (2-3) scattered five hits over 6 1/3 innings, giving up one run and striking out six.
Walks have been a thorn in the Jays side. Toronto pitchers had issued 108 free passes going into play Sunday — second-worst in the majors — with Dickey tied for the MLB lead with 18.
But Dickey was in control Sunday. He threw 95 pitches, including 62 strikes, and didn't issue a walk for the first time since October 2012.
"When I have one to zero to two walks, it's usually going to be a pretty good day," he said. "And that's what I have to get back to and today was a step in that direction."
Relievers Steve Delabar and Esmil Rogers closed out the game for Toronto, which outhit Boston 9-6.
Lester (2-4) deserved better from his seven innings. He gave up four runs on five hits, striking out seven and walking none. He threw 120 pitches, 80 for strikes, as Boston (12-14) was denied its first sweep of Toronto since June 10-12, 2011.
The Boston left-hander came into the game with a 15-7 career mark against Toronto, having held the Jays to a .199 batting average.
It was the first win for Dickey since April 5 and came after three starts in which he went 0-2 with 13 walks in 13 1/3 innings. He used his fastball more than usual, knowing that Boston led the league in pitches seen.
"So I knew they were probably going to be patient. And nothing's worse than seeing a fastball down the middle from a knuckleball pitcher and letting it go," he added.
Some observers thought Dickey seemed irked at being pulled in the seventh inning. The pitcher, who has faded in some previous starts, said he's just "passionate" about what he does.
He acknowledged he had told both Gibbons and pitching coach Pete Walker to keep a close eye on him in case he did falter.
After the Jays went ahead 2-1 in the third, Dickey and Lester took turns mowing down the opposition.
It took some time but Toronto bats finally came alive, welcome news for Dickey who had only got five runs in support before leaving in his five previous starts.
Toronto increased its lead to 4-1 in the seventh on back-to-back doubles by Encarnacion and Lawrie and an RBI groundout by Sierra. Lester had retired 10 straight prior to the inning.
Reyes scored on an RBI single by Bautista — who extended his on-base streak to 25 games — in the eighth before Encarnacion drove in two more with another double.
Dickey retired his first five hitters before giving up a run on three straight singles with the RBI going to Jackie Bradley Jr. Lawrie tied it up with one swing of the bat in the bottom of the second, depositing a 3-2 Lester delivery into left-centre for his sixth homer.
Lawrie has just 17 hits this season but seven have been for extra-base hits.
Toronto went ahead 2-1 in the third on Cabrera's two-out RBI double, sending Josh Thole home. Thole, Dickey's personal catcher, singled down the left-field line and then advanced on Jonathan Diaz's sacrifice bunt.
Cabrera, who came into the game leading the majors in hits, now has 39 including 13 of the extra-base variety.
Dickey was slated to head home after the game, with a couple of bobbleheads under his arm for his kids.
"They're not going to be collectors at my house," he said. "The heads are going to be popped off by the end of the day."