Cam Thomas scored 33 points and Michael Porter Jr. had 31 for Brooklyn, who are 0-2.
Cleveland led by 25 points in the third quarter before the Nets rallied in the fourth.
Ziaire Williams hit a 3-pointer to make it 121-115 with 5:18 left before a short delay after a fan ran on the court.
Merrill missed a 3-pointer after play resumed, and Thomas’ layup cut the deficit to 121-117.
Mitchell, who was 10 for 15 from the floor, turned the ball over on the ensuing possession before Brooklyn rookie Egor Demin’s 3-pointer made 121-120 with 3:48 remaining.
Cleveland then took advantage of multiple missed shots by the Nets and scored six consecutive points to extend the lead 127-120 with 38 seconds remaining.
The Cavaliers shot 44 for 82 from the field and made 18 of 42 from 3-point range, including 9 of 11 in the third quarter.
Up next
Cavaliers: Host Milwaukee on Monday night.
Nets: Visit San Antonio on Sunday.
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AP NBA: https://apnews.com/hub/nba