Kole Calhoun and Will Brennan drove in one run apiece for Cleveland, which evened the series at one victory apiece with the rubber match set for Wednesday afternoon.
Royce Lewis hit a home run for the third consecutive game for the Twins.
Guardians left-hander Sam Hentges (3-2) earned the win with two scoreless innings of relief. He allowed two hits and struck out four.
Twins right-hander Pablo Lopez (9-7) drew his first loss in his past seven starts. He gave up three runs on eight hits in six innings, with three walks and five strikeouts.
Emmanuel Clase closed out the ninth inning to collect his 35th save for Cleveland.
Naylor opened the scoring with a solo shot to right field in the second. He hit a fastball 388 feet for his seventh homer.
One inning later, the Guardians increased their lead to 2-0 when Jose Ramirez scored on a wild pitch by Lopez.
Cleveland made it 3-0 in the fourth. Calhoun stepped to the plate with runners on second and third with one out, and he drove in a run on a groundout.
The Twins trimmed the deficit to 3-1 on Lewis' solo home run to lead off the bottom of the fourth. He turned on a 93 mph fastball for a 396-foot home run to left field. It was his ninth of the season.
The Guardians added another run in the seventh to make it 4-1. Andres Gimenez reached on a fielder's choice, stole second and scored on Brennan's single to center field.
Michael A. Taylor hit a solo homer for the Twins in the ninth to cap the scoring.
Guardians right-hander Gavin Williams exited his start after one scoreless inning because of right knee soreness.
Lewis, who set a Twins franchise record with grand slams in back-to-back games this week, had a chance to make it three in a row in the first. His attempt came up short as he popped out to second to strand the bases loaded.
—Field Level Media