The victory marked the first time the Sixers have won back-to-back games since they defeated lottery-bound Cleveland and Charlotte a little more than three weeks ago.
Williams, who finished with 21 points, 12 of them in the first half, was able to watch the closing moments from the bench because his teammates stepped up in the fourth quarter.
Coming off a career-high 26 points against Boston, Evan Turner looked as if he really belongs in the starting lineup after posting his third double-double (16 points and 12 rebounds, along with six assists) of the season.
Andre Iguodala also finished with a double-double (10 points, 10 assists), Jrue Holiday contributed 16 points, and Elton Brand had eight points, nine rebounds, and three blocks.
Paul Millsap led Utah (19-20) with 15 points.
The Sixers were coming off one of their better performances in quite some time, Wednesday's 32-point drubbing of the Boston Celtics, their largest victory over their Atlantic Division rival in 30 years.
They accomplished that without the services of Thaddeus Young, who missed Wednesday's game with an upper respiratory condition. But Young, one of the Sixers who had been playing better in recent games, looked fine on the way to 21 points Friday night to tie Williams for team scoring honors.
Early on the Sixers seemed to be having problems with their execution, as evidenced by four early turnovers they committed on the way to falling behind, 12-6.
But the Sixers seemed to get things under control the rest of way, played with more confidence, and cut the lead to just 27-25 at the end of the quarter.
Down by as many as eight points in the first quarter, the Sixers drew even at the 6:50 mark on a pair of Jodie Meeks free throws.
Brand and Holiday both failed to score in the first half. However, they combined to add nine points in the second quarter.
A perfect 4 for 4 from the field in the first half, Iguodala put down a slam dunk with just over one minute remaining to give the Sixers a 49-45 lead. But Millsap, who led the Jazz with 10 points at the break, responded with a dunk of his own to close the Sixers' halftime lead to just two points, 49-47.
A 7-0 run, capped by a technical foul free throw, gave the Sixers a 65-54 lead with 5:11 left in the third. And while the Jazz cut into the lead slightly, the Sixers maintained a 10-point edge heading into the fourth quarter.
Contact staff writer John N. Mitchell at email@example.com. Follow him on Twitter @JmitchInquirer. Read his blog at www.philly.com/deepsixer