The red-hot Cano and the visiting Yankees will now take aim at a fill-in starter as they look for a fourth straight victory Wednesday night.
New York (4-4) has amassed eight homers among 25 runs and 31 hits in this series. Cano is 7 for 10 with three homers and seven RBIs in the first two games.
The superstar second baseman hit two solo homers in an 11-6 victory Monday. He added two doubles and a homer among his four hits Tuesday in a 14-1 rout, the Yankees' most lopsided win in Cleveland since an 18-1 victory in 1931.
"When he hits the ball hard, it's usually for extra bases and drives people in," manager Joe Girardi said. "It does take some pressure off. I've seen him hit some balls in the last two days, I don't know how you can hit them any harder."
The Yankees reached Ubaldo Jimenez for seven runs over 4 1-3 innings Monday. That's the same number of runs Carlos Carrasco was charged with Tuesday over 3 2-3 innings before he was ejected for hitting Kevin Youkilis in the shoulder - one pitch after giving up a homer to Cano.
Indians manager Terry Francona did not believe the plunking of Youkilis - who played for Francona in Boston - was intentional. Carrasco apologized.
"It didn't look good," Francona said. "I understand the umpire's viewpoint. I think if you look at the video, he slipped. If you're on the other side, I understand it. But that's what happened."
Francona brought in Brett Myers to replace Carrasco. Myers, originally scheduled to start Wednesday night, also gave up seven runs over 5 1-3 innings.
Corey Kluber will make his season debut instead, with Carrasco being sent to Triple-A Columbus to make room. The right-hander, 2-5 with a 5.14 ERA in 12 starts last season, pitched five innings of one-run ball and struck out six in his only career start against New York, a 3-1 loss Aug. 24 at Cleveland.
Kluber hit Derek Jeter in the head with a pitch in that contest, and the currently injured Yankees shortstop was seen admonishing Kluber after the fact.
Jeter later said he didn't think he was hit on purpose.
Francona knows that it won't be easy for Kluber to slow down Cano.
"He's one of the best hitters in the league," Francona said. "It seems like you make a good pitch and he hits a single. You make a mistake and it's over the fence."
Eleven of New York's 18 hits Tuesday went for extra bases. Brett Gardner was 4 for 5 with three runs and Youkilis, Ichiro Suzuki, Lyle Overbay and pinch-hitter Brennan Boesch were the other Yankees to homer besides Cano.
Asdrubal Cabrera's sixth-inning homer was all Cleveland (3-5) could muster in reply. It helped the Indians avoid their third shutout loss of the season.
Nick Swisher has gone 3 for 6 with two walks for the Indians in his first games against his former club.
Yankees starter Ivan Nova (0-1, 7.71 ERA) hopes the run support continues as he makes his second start of the season. Nova yielded four runs over 4 2-3 innings Friday in an 8-3 loss at Detroit.
The right-hander's 5.68 career ERA in April is his highest in any month. He won his lone career outing against Cleveland, allowing two runs over seven innings of an 11-7 home victory June 10, 2011.