There were also wins for the Hornets, 76ers and Bulls.
Fournier’s 26-foot shot put the Knicks in front in their opening game of the season with 56.1 seconds left in the second extended period, while Derrick Rose sealed the victory.
Julius Randle topped New York’s scorers with 35 while Jaylen Brown hit 46 for the Celtics assisted by 20 from Jayson Tatum, whose missed jumpshot at the end of the first period of overtime proved costly.
The Charlotte Hornets put 24 points on the board without reply in the third quarter as they came from behind to beat the Indiana Pacers 123-122.
LaMelo Ball scored 31 points, including seven three-pointers, while Gordon Hayward added 27 in the victory.
The Philadelphia 76ers were without Ben Simmons for their trip to New Orleans but overcame a Zion Williamson-less Pelicans 117-97 with Joel Embiid and Furkan Korkmaz scoring 22.
Zach LaVine scored 34 to help the Chicago Bulls to a 94-88 win over the Detroit Pistons, the Washington Wizards swept past the Toronto Raptors 98-83 and Ja Morant scored 37 to help the Memphis Grizzlies to a 132-121 win over the Cleveland Cavaliers.
Karl-Anthony Towns had a double-double with 30 points and 10 rebounds for the Minnesota Timberwolves in a 124-106 win over the Houston Rockets, the San Antonio Spurs saw off the Orlando Magic 123-97 and the Utah Jazz beat the Oklahoma City Thunder 107-86.