Cabrera hit a two-run homer, Jason Donald added a solo shot and the Indians beat the Blue Jays 5-4, their sixth win in seven games against Toronto.
"We played really good ball these last couple of games," Cabrera said. "We want to play like that the whole rest of the season."
Cleveland has traded pitchers Jake Westbrook and Kerry Wood, outfielder Austin Kearns and infielder Jhonny Peralta in the past week, depleting the team of much of its veteran presence and leaving just two players (Shelley Duncan and Travis Hafner) over the age of 30.
When it comes to filling the leadership void, Indians manager Manny Acta said Cabrera "brings a lot to the table."
"He's the right guy to start leading these kids out here," Acta said. "He's been in the big leagues for close to four years, he's been in the playoffs with the Indians. I'm expecting him to take a bigger role."
Donald said he considers Cabrera a clubhouse role model.
"He's got some time here," Donald said. "He came up with Cleveland, he's been in the big leagues for a couple of years. He's a guy that we look to and he's done a great job. He's got a lot of energy and that's a guy you can feed off of."
Called up from Triple-A Columbus to make his second big league start on three days' rest, right-hander Jeanmar Gomez (2-0) allowed two runs and five hits in five innings. He walked two and struck out two.
"The kid made the best of the 85 pitches that he had and it was five good innings," Acta said.
Gomez took the roster spot of Wood, who was traded to the New York Yankees on Saturday, and stepped into the rotation after the Indians moved Josh Tomlin up by a day when Westbrook was scratched from Saturday's start and traded to St. Louis.
Five Cleveland relievers combined to work the final four innings. Tony Sipp pitched 1 2/3 innings, Frank Hermann got one out in the seventh, Rafael Perez got two outs in the eighth and Joe Smith got the third. Chris Perez wrapped it up in the ninth for his 12th save and second in two games.
Perez, who got out of a bases-loaded jam in Saturday's 2-1 win, was threatened again in this one but still extended his scoreless streak to 13 1/3 innings. Travis Snider hit a leadoff single and advanced to second on Dewayne Wise's sacrifice, but Perez escaped when Escobar flied out and Bautista struck out swinging.
The Indians jumped on Toronto right-hander Jesse Litsch (1-5) in the first. Trevor Crowe drew a leadoff walk and scored when Cabrera hit a two-run homer that bounced off the top of the right-field wall, his second.
Donald said the Indians had some fun with Cabrera when he got back to the dugout.
"We thought it had a good chance off the bat," Donald said. "I didn't think it was going to come that close to not getting out. Guys were joking around and laughing and stuff. I said, 'Is that what you call a wall-scraper or a wall-bouncer?'"
Hill opened the second with a homer off the left-field foul screen, his 15th.
Cleveland regained the lead in the fifth. Crowe doubled, Litsch slipped while trying to field Cabrera's bunt single and Shin-Soo Choo walked before left-hander Brian Tallet came on in relief. Tallet walked Carlos Santana to force in a run, and another scored when Matt LaPorta grounded into a double play.
Donald hit a two-out solo drive to left in the sixth, his third.
Escobar and Bautista cut it to 5-4 with back-to-back drives in the seventh, the eighth time this season the Blue Jays have hit consecutive homers. Escobar chased Sipp with a shot to left, his third, and Bautista drilled Hermann's first pitch down the left-field line for his 32nd home run.
"They made it a ballgame really quick with two swings there," Acta said.
The Blue Jays lead the major leagues with 161 homers and have gone deep in 13 consecutive games, hitting 31 in that span.
Litsch has won just once in nine outings since coming off the disabled list June 9 after missing more than a year following elbow surgery. He allowed four runs and six hits in four-plus innings.
"I still don't see the velocity I had before," Blue Jays manager Cito Gaston said. "His control is not as good as it was before."
Hafner (shoulder) missed his fourth straight start but took batting practice before the game. Jordan Brown made his major league debut as Cleveland's DH. ... Toronto OF Fred Lewis and 3B Edwin Encarnacion were held out of the starting lineup. Snider played left, Wise was in right and Bautista moved to third.