Carrasco struck out a season-high 14, Jason Kipnis and Rajai Davis hit solo home runs and the Indians matched a franchise record by winning their 13th consecutive game Thursday night, beating the Toronto Blue Jays 4-1.
Manager Terry Francona said Carrasco "pitched his heart out."
"That's a good lineup and he really pitched well," Francona said.
Cleveland's streak is the longest by any team this season, and the longest for the Indians since they won 13 straight in August 1951. Cleveland also won 13 in a row in 1942.
It's the longest streak by an AL team since Oakland won 20 straight in 2002.
The Indians went 22-6 in June, the best single month in team history.
"It feels great," Carrasco said. "We've played really hard and we need to continue that. Everything is coming together."
Indians starting pitchers are 10-0 during the streak, and Cleveland has outscored its opponents 80-26.
"We expect to win every night we step on the field," Davis said. "We've just got to keep that mindset and not worry about everything else."
Still, Francona doesn't want his players getting too excited.
"You turn the page pretty quick," he said. "If you start taking time to sit back and evaluate (what happened) two weeks ago, then tomorrow might not be so good."
Coming off a four-hit shutout victory at Detroit, Carrasco (4-2) allowed one run and three hits in 7 1/3 innings to win back-to-back starts for the first time since April 13 and 19. The right-hander was sidelined from April 25 to June 2 with a strained left hamstring.
"No doubt about it, it was Carrasco's night," Blue Jays manager John Gibbons said. "He was on."
Carrasco's career-high in strikeouts is 15, set last Sept. 25 at Kansas City. Against Toronto, he struck out four straight in the third and fourth innings, then fanned six straight in the sixth, seventh and eighth.
Bryan Shaw replaced Carrasco after Darwin Barney ended the strikeout streak with a double. Shaw struck out pinch hitter Russell Martin, walked Ezequiel Carrera, then fanned Josh Donaldson to end the inning.
Cody Allen got the last three outs for his 17th save.
Davis hit a leadoff shot off R.A. Dickey in the second and Kipnis hit a one-out drive in the third.
"They ran into a few that didn't do much," Dickey said.
Dickey (5-9) allowed three runs and eight hits in seven innings. The knuckleballer has allowed six home runs in his past two starts, all of them solo shots. He is 0-6 with a 5.14 ERA in eight home starts.
Donaldson provided Toronto's only offense with a two-out solo homer off Carrasco in the fourth.
Toronto struck out 10 or more times for the 24th time this season. They did it 28 times in all of 2015. The Blue Jays finished with 17 strikeouts, their most since fanning 17 times against Texas on July 18, 2014.
Kipnis extended his hitting streak to a season-high 12 games.
Cleveland and Toronto met for the first time since longtime Indians employee Mark Shapiro took over as president of the Blue Jays last November. Shapiro also hired former Cleveland colleague Ross Atkins to serve as Toronto's GM. Shapiro was with the Indians for 24 years before joining Toronto.
Indians: OF Michael Brantley (right shoulder) continues to hit in the cage and do soft toss drills without pain, manager Terry Francona said. Brantley, who is not with the team, resumed hitting drills earlier this week after setbacks in May and June.
Blue Jays: Prior to the game, LHP Brett Cecil was activated off the 15-day DL and RHP Ryan Tepera was optioned to Triple-A Buffalo. Cecil missed 42 games with sore left triceps. Cecil relieved Dickey and pitched a perfect eighth. ... SS Troy Tulowitzki got the day off.
Indians: RHP Josh Tomlin (9-1, 3.32) starts for Cleveland in a Canada Day matinee on Friday. Tomlin is 1-0 with a 5.19 ERA in three career starts against Toronto.
Blue Jays: RHP Marcus Stroman (6-4, 5.33) has allowed 38 earned runs in his past eight starts and has lost three of his past four decisions.
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