"You wish it would have went different. You hope for it to be different," Dickey said. "Opening Night, everybody is here, full of energy."
Cabrera hit a two-run homer off Dickey, Masterson pitched six innings and the Indians ended their streak of Opening Day losses at four.
Cleveland won its opener for the first time since beating the Chicago White Sox in 2008. The Indians had dropped eight of their past 10 openers.
Excited by the winter acquisitions of Dickey, Jose Reyes and other All-Stars, fans in Toronto were eager to see the revamped roster in action. They sellout crowd of 48,857 cheered as Dickey walked out to the bullpen to warm up before the game, and roared even louder during player introductions.
"The welcome that I got from the fans was borderline supernatural," Dickey said. "It was pretty awesome. Deep down, you want so badly to give them a great show and you want to entertain them."
Instead, Masterson and three relievers combined to hold Toronto to just one hit after newcomer Melky Cabrera's leadoff single in the third, a two-out double in the ninth by catcher J.P. Arencibia. Colby Rasmus followed by striking out to end the game.
"We just couldn't get anything going against their pitching," Blue Jays manager John Gibbons said.
Masterson (1-0) allowed one run and three hits in six innings, ending his night by retiring 11 straight batters. The right-hander walked four and struck out five.
"He was probably pitching better when we took him out than he was earlier in the game," Indians manager Terry Francona said. "I just thought that was enough for a first start."
On Opening Day last year, Perez allowed three runs in the ninth against Toronto as the Blue Jays rallied to force extra innings, winning it in the 16th on a three-run homer by Arencibia.
There was no ninth-inning drama this time, but Francona was still worked up in his return to the dugout following a season in the broadcast booth.
"I was so nervous the whole game, it surprised me," Francona said. "I came to realize early in the game how much I care about these guys already that it hit me like a ton of bricks and I was a nervous wreck. I went through three things of tobacco. My tongue is four sizes too big right now."
Dickey (0-1) allowed four runs, three earned, and five hits in six innings. The knuckleballer walked four and struck out four.
"That's not an easy guy to face," Francona said. "He's a really good pitcher. We certainly didn't knock him around the ballpark, but we did enough to win."
Dickey's four walks were his most since May 6, 2012, when he walked four against Arizona.
"I think I walked four guys all of spring training so that was an anomaly for me," Dickey said.
In 33 starts last season for the New York Mets, he issued more than three walks just twice -- he was traded to Toronto in the offseason.
It was a rough night for Arencibia, who was charged with three passed balls in the first two innings as he struggled with Dickey's knuckleball.
"Early it was dancing a ton," Arencibia said. "It was really darting every way possible. It made it tough."
Arencibia's two passed balls in the second helped Cleveland score the first two runs of the game. Michael Brantley singled and went to second on a passed ball before Mark Reynolds drew a one out walk before a second passed ball put runners at second and third. Lonnie Chisenhall hit an RBI grounder and Drew Stubbs followed with an RBI single.
That prompted Vancouver Canucks goaltender Roberto Luongo, the subject of trade rumors linking him with the Toronto Maple Leafs and other teams, to tweet about Arencibia's troubles, saying, "Maybe the Blue Jays need a goalie to catch RA Dickey? Just sayin......."
After the third, backup catcher Henry Blanco suggested Arencibia turn his catching stance to the side, giving him more lateral range. That adjustment, and better command from Dickey, prevented any further passed balls.
Gibbons said he wouldn't hesitate to start Arencibia behind the plate in Dickey's next start.
"I wouldn't see why not," Gibbons said. "Anytime you're catching a knuckleball, I don't care who it is, you're going to miss some balls."
Toronto loaded the bases with none out in the third but could only push across one run, with Melky Cabrera scoring on Adam Lind's double play grounder, a hot shot that was speared by Asdrubal Cabrera, who flipped to second from a prone position to start the twin killing.
Francona called it "a huge play" and Gibbons said it was "a game changer."
Cleveland added to its lead in the fifth when Michael Bourn led off with a single and Cabrera drilled a high knuckleball into the right field bullpen.
"It's not easy," Cabrera said of facing Dickey. "He's got really good stuff. I'd say I got lucky there."
The Indians put runners at second and third with one out in the eighth, but Sergio Santos struck out Reynolds and Chisenhall to end the threat.
Cleveland LHP Scott Kazmir has a sore abdominal muscle and might miss his first scheduled start, this Saturday at Tampa Bay. The Indians selected Kazmir for the 25-man roster and optioned left-hander Nick Hagadone to Triple-A Columbus. ... Cleveland also outrighted LHP David Huff to Columbus and had OF Ezequiel Carrera claimed off waivers by Philadelphia. ... Singer Geddy Lee of the rock group Rush threw out the ceremonial first pitch. Rush will be inducted into the Rock and Roll Hall of Fame on April 18... Former Blue Jays Joe Carter and Duane Ward attended the game.