Utah made its first six shots, including a pair of 3-pointers by Hayward, and opened a quick 14-2 lead.
Philadelphia rallied, however, after coach Doug Collins subbed out his entire starting five with 7:35 left in the opening quarter.
Charles Jenkins scored five points and Arnett Moultrie added four as Philadelphia got within four, 27-23.
In the second quarter, Derrick Favors scored seven quick points.
The Jazz opened a 42-29 lead and, despite converting only one of their next eight possessions, they got to halftime with a comfortable 58-42 advantage after closing on a 13-2 run.
Foye scored 13 points in the first half and Hayward finished with 10. Spencer Hawes topped the 76ers with 12.
Early in the third quarter, Philadelphia closed to within 12, when Jrue Holiday's 3-pointer made it 62-50.
The Jazz countered with baskets by Al Jefferson and Paul Millsap, however, to stop the 76ers' momentum and regain control.
Utah took an 85-69 lead into the fourth quarter, where the Jazz extended their advantage to 95-73 with eight minutes left and cruised to a victory that snapped a four-game losing streak.