Oakland also hit three homers, but fell short of a comeback after Khris Davis went deep off Indians closer Cody Allen with one out in the ninth inning for his team-leading 16th homer. The A's stranded the potential tying run to drop to 7-18 on the road.
"I thought [Carrasco] was very good," Indians manager Terry Francona said. "He fell behind a couple hitters and kind of laid a fastball in there, and they hit the two solos. Then they end up with three solos. But other than that, I thought he was really good. Very good breaking ball, used it when he was supposed to. I thought he did a really good job. [He] got the double-play ball when he needed it."
Cleveland's power parade began when Austin Jackson christened the third inning with a home run, and continued in the fourth with back-to-back blasts from Carlos Santana and Edwin Encarnacion. The Indians kept at it with three more hits before Mengden recorded his only out of the fourth, a sacrifice fly from Jackson.
"It feels good," Encarnacion said of the back-to-back homers. "It's something that our team needs. They need to know that we're doing our work, and that we can do that work that's necessary to help us win a game."
Mengden, recalled from Triple-A Nashville ahead of the game to replace an injured Kendall Graveman, was responsible for five runs and seven hits in 3 1/3 innings. Carrasco, meanwhile, picked up his first home victory of the season and fifth overall, limiting the A's to four hits across seven strong innings, including back-to-back homers by Yonder Alonso and Ryon Healy in the seventh.
"Besides feeling well, I gotta be better than that," Mengden said. "Five runs by the fourth inning, and it's just tough when Carrasco is throwing as well as he did and having [Andrew] Miller and Allen at the back end of the bullpen. It's tough putting the guys in a hole like that."
MOMENTS THAT MATTERED Knocked around: Mengden, hoping to find his footing after yielding hits to his first four batters of the fourth for a 3-0 Indians lead, instead got drilled in the left calf by a Bradley Zimmer line drive. The ball deflected off Mengden and traveled into the outfield for a double, putting runners at second and third. Mengden stayed in the game after a visit from the club's head trainer but only for one more batter, departing after 72 pitches.
"I don't think he was tired," A's manager Bob Melvin said. "More than anything, he just started finding the middle of the plate. Early on he had a good mix and looked confident. Balls were more on the corners. A few balls caught the middle of the plate, and they had him on the run there a little bit."
Closing time: Following Carrasco's exit, with the right-hander having limited the damage in the seventh inning to maintain a sizeable lead, the Indians turned to their lights-out bullpen to seal the deal. Left-hander Miller struck out the side in the eighth in predictable fashion, and Allen rebounded from Davis' homer to lock down his 14th save, stranding two. Indians pitchers combined for 12 strikeouts on the day.
"No, Cody's fine. He's fine. In my opinion, he's one of the best in the game. Now sometimes you're going to give up runs. Today, before the home run, he threw a great breaking ball. Probably this far off the plate. Sometimes those things happen. He's OK."
-- Francona, on Allen's save
"Austin's been here for three days and he's staying in the middle of the field so well. When hitters do that, they generally cover more pitches. Whether it's a sacrifice fly to deep right-center or a home run today, but his swings have been pretty consistent just because he's staying in the middle of the field so well."
-- Francona, on Jackson's day at the plate
SOUND SMART WITH YOUR FRIENDS
With Jackson's third-inning solo homer, the Indians have now hit at least one home run in 14 consecutive games (25 home runs total) dating back May 14. That is the team's longest streak since 2007, when it homered in 15 consecutive games.
BRANTLEY EXTENDS HIT STREAK
In the seventh, Indians left fielder Michael Brantley extended his hitting streak to 13 games with a ground-ball single to center. Brantley owns the longest hit streak by an Indians player this season.
WHAT'S NEXT Athletics: Right-hander Sonny Gray will be on the mound in Tuesday's 3:10 p.m. PT matchup with the Indians at Progressive Field. Gray is 2-1 with a 2.59 ERA in five career starts against Cleveland.
Indians: Right-hander Trevor Bauer (4-4, 6.30 ERA) will take the mound in the second game of the series, with first pitch slated for 6:10 p.m. ET. Bauer is coming off a no-decision against the Reds, during which he allowed two runs on four hits and two walks in 5 1/3 innings.