Cousins, who played about 17 minutes, had 13 points in the third quarter when the Kings (1-1) used a 33-26 advantage to take an 89-76 lead into the fourth.
Kyle Lowry had 25 points and six assists and DeMar DeRozan had 23 points for Toronto (1-1), which had a franchise-record 48 wins last season. Jordan Hamilton added 12 points.
Omri Casspi scored 15 points, rookie Nik Stauskas had 13, Ben McLemore added 12 and Jason Thompson had 11 points and nine rebounds for the Kings. Darren Collison had 10 points and five assists as Sacramento shot 55 per cent.
Cousins got called for a technical foul in the third quarter after getting tangled up Toronto's Tyler Hansbrough, who was called for the foul.