Nick Swisher followed Cano's homer with a solo shot, marking the fourth time the Yankees have hit back-to-back homers this season. Backup outfielder Dewayne Wise also went deep off Tomlin, who was battered for six runs in three innings.
"This team is designed to hit home runs," Swisher said. "That's the one thing we do a pretty good job of. Everyone talks about the runners in scoring position, but a solo shot is just as good as an RBI single with a runner on second."
For Cano, the contest marked the continuation of a power surge that has seen him homer in six of his last eight games on his way to a .329 batting average with 16 RBIs in June.
"He's just making great contact," Yankees manager Joe Girardi said. "He's seeing the ball well, he's getting his pitch and he's not missing it. That's the bottom line."
The offensive eruption from the Yankees, who own the Majors' most homers with 115 through 71 games, produced a breezy night for Hiroki Kuroda, who worked seven-plus innings and picked up his seventh victory.
"That was Hiro's game today," Swisher said. "For him to do what he's been doing for us all year long; what a pickup in the offseason for us. That was huge."
Kuroda entered the eighth with a shutout and held the Indians to just five hits -- including a double by former Yankee Johnny Damon -- in the right-hander's first career start against the Tribe.
"After they got out to that lead, he was pumping the first-pitch strike," Damon said. "And then his splitter was really good. He knew his splitter was good and the pitches we had a chance to hit well, we didn't until the eighth inning."
Kuroda didn't feel his cutter was all that sharp in the bullpen, but catcher Chris Stewart disagreed and kept calling for it, with winning results.
"I saw a lot of people swinging at that from the beginning of the game," Kuroda said through an interpreter. "I didn't think I was able to get the rhythm that I wanted, but I was ahead of the count a lot of the time, so I think it was really effective."
The Indians finally scored in the eighth as Kuroda opened the inning allowing hits to Lonnie Chisenhall and Shin-Soo Choo. Jason Kipnis knocked in the run with a sacrifice fly facing Clay Rapada.
It was an inning that saw Swisher have a great time, making all three catches in right field -- one on a slide and one after a long run toward the corner. The giddy Swisher earned an ovation after he came off the field and again despite striking out the next inning.
"I don't know if I've made three outs in an inning like that, and the place was going crazy, man," Swisher said. "It was great."
Winning for the third time in his last four starts, Kuroda struck out seven and walked two, marking his ninth start this season of six or more innings while allowing two runs or fewer.
"I thought he had real good command of his fastball and his slider tonight," Girardi said. "Those were his two key pitches, and that's kind of been his M.O. the last seven or eight starts."
On an evening when Girardi rested Alex Rodriguez and allowed Curtis Granderson to take a half-day as the designated hitter, the club's depth played a role as Wise -- playing center field -- enjoyed his best night as a Yankee.
The 34-year-old journeyman crushed a two-run homer in the second inning and legged out a run-scoring triple in the sixth facing Scott Barnes.
"He always comes in, works hard and never complains about playing," Cano said. "Seeing him in the lineup tonight, we were happy and excited."
Wise had notched just five total bases all season before Monday evening, playing mostly as a defensive replacement or pinch-runner after attending camp this spring as a non-roster invitee.
"I was just happy I walked in today and saw my name in the starting lineup," Wise said. "To be honest, I think the team was more happy than I was. It turned out to be a good day."