Francona returned to the dugout after being hospitalized for a few hours Tuesday night.
Puig chose to appeal the suspension, and was in the lineup on Wednesday. There was no immediate word following the game on Francona's condition.
Andrew Miller hadn't given up a home run this season prior to this week.
In the bottom of the seventh inning, the Indians evened the score at 2-2 when third baseman Jose Ramirez hit a line-drive home run just inside of the foul pole in right field.More news: Defending champion Johnson out of US Open
The Marlins have handled Garrett, 19, carefully since selecting him seventh overall in the 2016 draft, keeping him out of pro action last season and delaying the start of his 2017 until May to limit his workload.
The victory gives the Dodgers the best record in the National League at 41-25, as they remain percentage points ahead of the Colorado Rockies for first place in the NL West.
The Indians go into Thursday at 31-31 - the first time they have been.500 since April 18, when they were 7-7. Mike Piazza had five such games in 1993 and Corey Seager had four games in 2016. It will also be Hill's first career start at Progressive Field.
Dodgers: 1B Adrian Gonzalez was placed on the 10-day disabled list with lower back discomfort. He was 0-2 with a 5.40 ERA in five starts for Los Angeles.More news: ICC Champions Trophy: India-Pakistan clash bigger than Ashes: Irfan Pathan
Dodgers starter Brandon McCarthy was charged with one run in 5 1/3 innings.
Wednesday will be Kluber's second career start against the Dodgers.
The climactic moment in the ballgame came in the sixth, when Miller left all three of his inherited runners stranded on a bases-loaded strikeout of Puig... Kluber is the seventh pitcher in Major League Baseball history to reach the milestone in less than 150 career games, and the fastest Cleveland Indian in franchise history to accomplish the feat.
So far against the Indians, the Dodgers have scored four total runs in the first seven innings of the first two games, and nine runs in the eighth and ninth innings combined. "He hung a slider, and I got it". "He's got to be able to make an adjustment (during games) because with all that traffic (hits and walks), you're going to pay for it sooner or later", Francona said. In 28 appearances, he is 3-1 with a 0.55 ERA.More news: Russian Federation inquiry: I'm under investigation
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