The Angels (67-77) won the series 3-1 despite being without banged-up star Shohei Ohtani for all seven games this week. They started three rookies for the second straight game.
The Guardians (68-76) are now 7 1/2 games behind the division-leading Minnesota Twins, who lost 2-0 to the New York Mets, in the American League Central with just 18 games to play.
The Angels went up 1-0 in the first inning when Randal Grichuk doubled, moved to third on a groundout and scored on Mike Moustakas' sacrifice fly.
Kole Calhoun — an Angel for the first eight years of his career — tied it for Cleveland in the second with a 426-foot homer to right-center, his fourth of the season and seventh against the Angels since leaving the team as a free agent in 2019.
Los Angeles went ahead 2-1 in the third when Kyren Paris beat out a single to first, moved to third on two consecutive balks by Cleveland right-hander Tanner Bibee and came home on Grichuk's RBI grounder.
Rosenberg (1-1), making just his third major league start, tossed five innings of one-run ball, giving up six hits and a walk with four strikeouts.
Bibee (10-4) took a hard-luck loss, allowing just two hits and two runs in seven innings with eight strikeouts and no walks, retiring the last 14 Angels he faced. But the third-inning balks proved to be decisive.
The Angels got three scoreless innings of relief from Andrew Wantz, Ben Joyce and Jimmy Herget before Carlos Estevez notched his 30th save with a 1-2-3 ninth.
The Guardians got two hits apiece from Calhoun, Jose Ramirez and Andres Gimenez but couldn't cash in enough of their runners.
—Field Level Media