Kyrie Irving led the nets on the night scoring 27 points, 7 rebounds and 9 assists as Harden finished with 22 points, 7 rebounds and 10 assists.
Altman inherited Cleveland's GM job when David Griffin stepped down and was thrown into the fire to figure out a trade for Kyrie Irving.
Cleveland led going into the fourth quarter, fell behind by three, then went on a 14-2 run to take a comfortable lead.
Losing Rubio is a major blow to Cleveland, which currently sits as the East's No. 5 seed with the league's fourth-best point differential.
Jaylen Brown scored 34 points and the Boston Celtics beat depleted Cleveland 111-101 on Wednesday night to end the Cavaliers' winning streak.