Cleveland rocked McGuire (0-2, 7.11) for three runs from the first three batters, forcing the Angels rookie from the game after just 25 pitches. Francisco Lindor delivered a leadoff single and Michael Brantley walked before Ramirez slugged a 3-2 fastball 423 feet to the seats in right. It was his 33rd home run of the year.
Brad Hand pitched the ninth inning for his 27th save, allowing a run on two hits, retiring L.A.'s dangerous designated hitter, Shohei Ohtani, on a grounder before striking out David Fletcher to end the game.
Ramirez again is tied with Boston's J.D. Martinez for the major league lead in homers, and upped his team-leading RBI total to 82. His 12 first-inning home runs this season are an Indians franchise record, breaking a tie with Al Rosen (11 in 1953).
"Some guys kind of warm into the game," manager Terry Francona said. "He's dangerous right from the very first pitch."
Ramirez's 156 extra-base hits since the start of 2017 lead the majors. Lindor, who doubled in the second inning, has 145 extra-base hits to rank second in that span.
"That guy's a competitor," reliever Cody Allen said of Ramirez. "He wants to be great and he wants to win just as bad or worse than anybody."
The Indians loaded the bases after Ramirez's home run, but failed to add any more runs in the first, as Los Angeles reliever Taylor Cole struck out Melky Cabrera and retired Roberto Perez and Leonys Martin on grounders. Cole worked 3 2/3 shutout innings of relief, allowing a hit and striking out three. His effort kept the Angels in the game, and allowed manager Mike Scioscia's offense time to get on track.
"We did a good job early, then we left some runners on from there," Francona said. "We had a chance to spread it out early and we didn't. We had a couple other chances to tack on and we didn't. But we held on."
Allen worked 1 2/3 innings of scoreless relief, entering in the seventh with the bases loaded and one out. He retired Andrelton Simmons on a pop out and got Fletcher on a grounder to third. Allen then worked around a Kaleb Cowart single to get out of the eighth unscathed.
"That's really good to see," Francona said. "Get him in that mode where he just comes in and competes and we got five outs. And he didn't throw a ton of pitches. That was exciting to watch."
Indians starter Shane Bieber (6-2, 4.58) tossed 5 2/3 innings, allowing two earned runs on seven hits with a walk and seven strikeouts. He pitched out of a jam in the fourth after allowing back-to-back hits by Andrelton Simmons and Fletcher with one out. Bieber struck out Francisco Arcia and Cowart to end the frame.
Bieber said once he realized that he did not have a good feel for his breaking ball, he and catcher Roberto Perez decided to move his fastball around.
"Especially late in the counts, and try to make good pitches down in the zone and up in the zone when I needed to," Bieber said. "My slider was the worst it's been in a little while. So, I was depending on the breaking ball a little bit more and really needed to command the fastball better."
Bieber also got some help defensively from right fielder Cabrera, who made a pair of diving catches in the third inning and opened the fourth by snagging a blast off the bat of Ohtani before crashing up against the outfield wall. Indians fans in right field rose to their feet after each grab, giving Cabrera a standing ovation for his effort.
"He was all over the place," Francona said. "That was kind of cool to hear the way (the fans) responded to it, too. He did a good job."
Cabrera went 1-for-3 at the plate with a base hit in the sixth inning. Pinch-runner Brandon Guyer turned that hit into an insurance run by scoring from first base when Jason Kipnis doubled to the gap in left center off L.A.'s Cam Bedrosian.
The Indians thought they had added a run in the second inning when Lindor tagged and scored from third on a line drive to center field by Edwin Encarnacion. With Ramirez running from first base on the play, Encarnacion smoked a ball to center that Eric Young Jr. caught. Ramirez was not able to get back to first base in time to avoid the inning-ending double play, but home plate umpire Nic Lentz originally ruled that Lindor crossed the plate with Cleveland's fourth run before the out at first took place. Scioscia challenged the ruling, and replay showed that Ramirez was retired before Lindor scored, negating the run.
What it means
Cleveland evened the season series at 3-3 against Los Angeles and has won 14 of its last 17 games against the Angels. The Indians have won six consecutive series finales, including five straight at home. Tribe starting pitchers are 24-4 in series finales this year.
McGuire threw 25 pitches, 13 (52 percent) for strikes. Bieber threw 94 pitches, 62 (66 percent) for strikes.
Thanks for coming
The Indians and Angels drew a crowd of 28,993 to Progressive Field. First pitch was at 1:11 p.m. with a temperature of 84 degrees.
The Indians welcome Minnesota for a four-game series at Progressive Field, as Trevor Bauer (10-6, 2.34 ERA) takes the mound against Twins starter Kyle Gibson (5-8, 3.47) on Monday night. Bauer is 1-1 with a 3.75 ERA in two starts against Minnesota this season.