Gordon Hayward racked up 20 points, three rebounds and two assists as his side came from behind at half-time to wrap up their first 4-0 series win in eight years.
Marcus Morris and Jayson Tatum also dominated for the visitors, both finishing with 18 points.
The Celtics will go on to face either the Milwaukee Bucks or the Detroit Pistons, with the Bucks leading their series 3-0.
The Portland Trail Blazers head home to the Moda Centre with a 3-1 series lead after a 111-98 win over the Oklahoma City Thunder.
In the night's other game, the Toronto Raptors edged towards the second round with a 107-85 win over the Orlando Magic.
Kawhi Leonard finished with 34 points to lead his side to a 3-1 series lead ahead of game five on Tuesday at the Scotiabank Arena.