Japanese rookie Murakami belted his first MLB postseason homer to take the White Sox to a 2-0 lead in the fourth inning, launching a pitch from Parker Messick 440 feet to the right-field seats at Cleveland's Progressive Field.
The towering shot also scored Miguel Vargas, who had singled to left field to open the frame.
"It was a perfect home run," Murakami said. "I just hit it really nicely."
The surprising White Sox added a third run in the top of the seventh, when Kyle Teel scored from first base on Colson Montgomery's double down the left field line.
Cleveland had their chances, leaving the bases loaded in both the third and fourth innings. They stranded seven runners in all as the White Sox took a 1-0 lead in the best-of-five American League division series, which continues in Cleveland on Monday.
The White Sox - carrying the hopes of lifetime fan Pope Leo XIV - are aiming to continue one of the most remarkable turnaround seasons in baseball.
After three straight seasons with 100 or more defeats, the White Sox finished the regular season with an 84-74 record, snagging the sixth seed in the American League.
In their first playoff series since 2021, they ousted the Houston Astros in two games in the Wild Card round.
Murakami has been a key contributor for the young team, belting 35 home runs in the regular season.
The 26-year-old arrived in Chicago from Japan on a two-year, $34 million deal three years after he became the youngest Triple Crown winner in Japanese professional baseball history in 2022.
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