The Celtics improved to 3-0 against their Eastern Conference rivals this season and broke a two-game skid, with Hayward recording 26 points and Al Horford adding 23.
A three-pointer from the corner by Hayward helped put Boston 105-103 up with 1:50 left to play, and despite chances for the 76ers to tie the game, the Celtics held on to take the win.
The Golden State Warriors claimed a fifth straight triumph, beating the Utah Jazz 115-108.
A 24-6 run in the fourth quarter helped the Warriors surge ahead, with Stephen Curry making back-to-back three pointers.
Kevin Durant led the way with 28 points, while Curry had 24 and Klay Thompson added 22.
The Orlando Magic took a fourth consecutive win for the first time since 2015, routing the New Orleans Pelicans 118-88.
Nikola Vucevic finished with 25 points and 17 rebounds, while Jonathan Isaac had a career-high 20 points.
The win puts the Magic just 1.5 games behind the Detroit Pistons for the final Eastern Conference play-off spot.
Meanwhile, a triple-double from LeBron James was not enough to clinch victory for the Los Angeles Lakers.
The Lakers fell to a 117-113 defeat to the Atlanta Hawks, who had previously lost three games in a row.
James scored 28 points, 16 assists and 11 rebounds for the Lakers, while Trae Young and John Collins both had 22 points for Atlanta.
The San Antonio Spurs ended a four-game losing streak by edging the Memphis Grizzlies 108-107.
Patty Mills scored a season-high 22 points, while LaMarcus Aldridge finished with the same.