Oscar Gonzalez and Andres Gimenez each had three hits as AL Central-leading Cleveland (76-65) moved 11 games over .500 for the first time since September 2020.
The Angels (61-82) clinched their seventh straight losing season, matching the team record set from 1971-77.
With Amed Rosario aboard after a leadoff single, Ramirez drove a 3-1 slider from Ryan Tepera (4-3) deep to right for his 27th homer. The All-Star third baseman also leads the Guardians with 111 RBIs.
''In reality, we're in a rebuild, but it's a bit different when you have very talented players that know how to play the game the right way,'' Ramirez said. ''It's fun to see them, and as long as we keep playing our way, it's going to be fun to watch.''
The Guardians opened a four-game lead over the Chicago White Sox, who lost 3-0 to last-place Colorado. The win streak for Cleveland matches a season high.
''Ramirez does a little bit of everything and he's really tough to pitch to,'' Angels interim manager Phil Nevin said. ''That's why I walked him two or three times in this series already, but in that situation, you can't put the winning run on second in Rosario.''
Trevor Stephan (5-4) recorded three outs for the win, and James Karinchak worked the ninth for his third save. Emmanuel Clase, who has an MLB-best 35 saves, was unavailable after pitching four times in the previous five days.
Luis Rengifo led off the ninth with a double for Los Angeles, but Karinchak retired the next three batters.
''We're trying not to overdo people, but the way we play, there's a lot of close games,'' Cleveland manager Terry Francona said. ''We're trying to manage about nine different things with our pitching staff.''
Mickey Moniak hit a two-run homer for the Angels, and Mike Trout had an RBI single in their fourth straight loss. Shohei Ohtani went 1 for 4 with an eighth-inning double.
Moniak went deep in the third for his third homer since he was acquired in an Aug. 2 trade with Philadelphia. Moniak was selected by the Phillies with the No. 1 overall pick in the 2016 amateur draft.
Los Angeles opened a 3-1 lead when Moniak scored on Trout's base hit in the fifth.
Cleveland got one back in the bottom half when Gimenez singled and scored on Austin Hedges' double-play ball. Gimenez singled again in the seventh and scored the tying run on Tyler Freeman's double off Jimmy Herget.
''There are no better veteran leaders, in my opinion, than the guys in our clubhouse,'' Freeman said. ''Jose is a fireball and someone to look up to, and all of them make us feel comfortable on the field or on the bus.''
Cleveland right-hander Cal Quantrill, who is 12-0 in his career at Progressive Field, allowed three runs and eight hits in seven innings.
''I know there have been some really special players this year, but Jose deserves to be in the (MVP) discussion,'' Quantrill said. ''At least in the discussion at the end of the year.''
Gonzalez opened the scoring with a solo shot in the second for his second homer in two days. The rookie has four homers and 11 RBIs over his last nine games.
Angels starter Patrick Sandoval pitched 5 1/3 innings of two-run ball. The left-hander has not allowed more than two earned runs in eight straight starts.
Los Angeles is 1-21 against the Guardians on the road since 2015, losing 11 straight.
Angels: SS Andrew Velazquez (right knee) will miss the remainder of the season after tearing his right meniscus Tuesday while fielding a Gonzalez grounder. Velazquez was placed on the 10-day injured list and will require surgery.
Guardians: LHP Anthony Gose (left elbow), who has been on the IL since July 3, underwent Tommy John surgery in Dallas. The former Tigers and Blue Jays outfielder was shut down six weeks ago after feeling discomfort in his triceps.
Angels: RHP Michael Lorenzen (6-6, 4.70 ERA) works the opener of a four-game set Friday against Seattle. Lorenzen went 5 2/3 innings, allowing an earned run, at Houston last week in his return from a two-month absence with a strained right shoulder.
Guardians: RHP Hunter Gaddis (0-1, 21.60 ERA) will be recalled from Triple-A Columbus to start a makeup game Thursday against the White Sox. Gaddis lost his only big league appearance on Aug. 5 against Houston, giving up eight runs in 3 1/3 innings.
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