James had 2-of-18 night from the field in the first game of the best-of-7 series. He had 12 points, nine rebounds and nine assists, but also 10 of Cleveland's 18 turnovers.
Sam Cassell scored 10 of his 13 points in the fourth quarter for the top-seeded Celtics, who committed 23 turnovers.
Zydrunas Ilgauskas had 22 points and 12 rebounds for the Cavaliers, who shot just 30.7 percent from the field.
Game 2 is Thursday night in Boston.