CLEVELAND—Cliff Lee became Cleveland’s first 20-game winner in 34 years, pitching a five-hitter for his second career shutout to lead the Indians to a 5-0 win over the Chicago White Sox on Monday night.

Lee (20-2) is the first Indians pitcher to reach 20 wins since Hall of Famer Gaylord Perry went 21-13 in 1974. The left-hander’s milestone win—his ninth straight victory—came exactly one year to the day that he was recalled from the minor leagues.

With a chance to join Perry as well as Hall of Famers Bob Feller and Bob Lemon in Cleveland’s record book as 20-game winners,...

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