Mitchell just missed a triple-double with nine rebounds and eight assists, after scoring 31 in his Cleveland debut.
The three-time All-Star whose arrival from Utah in a blockbuster trade sent expectations soaring also made four 3-pointers.
Evan Mobley scored 16. Kevin Love and Cedi Osman added 15 points apiece.
Love also made five of his team's 16 3-pointers and grabbed 12 rebounds.
Zach LaVine led Chicago with 23 points after missing the first two games with the team trying to manage his left knee after he had surgery in May.