The Celtics now hold a 2-1 lead over the Cavaliers in their Eastern Conference semifinals series.
Despite facing injury challenges, particularly with Luka Dončić nursing a knee sprain, the Mavs were able to hold off the Thunder at home.
Oakley has not been back at MSG since an altercation with security in 2017.
The Mavericks now have a 2-1 series lead and host Game 4 on Monday.