Derrick Favors finished with 17 points and seven rebounds, and Gordon Hayward and Marvin Williams each scored 14 for the Jazz, who fell to an NBA-worst 1-10.
Golden State (7-3) has taken advantage of a favorable home schedule so far this season.
The Warriors are 5-0 at Oracle Arena, with all five opponents playing the night before. Utah lost 91-82 to San Antonio on Friday night in Salt Lake City.
Warriors coach Mark Jackson cautioned his team not to take the Jazz lightly. With the same formula of swarming defense and sharp shooting that has carried the club since its surprising playoff run last spring, Golden State seemed to quickly turn the contest into a predictable rout.
The Warriors held leads of 27-13 after the first quarter and 51-34 at halftime, with Thompson and Iguodala each making three 3-pointers before the break. The defensive intensity stalled in the third quarter, though, and the nothing-to-lose Jazz capitalized.
Hayward's 3-pointer brought Utah within 61-54 with 5:37 remaining in the third. The teams traded baskets before Golden State slowly reasserted itself.
The Warriors outshot the Jazz 51.2 to 45.5 percent and outrebounded them 42 to 32 in a game that had far more drama than they preferred.
O'Neal, who has battled numerous knee injuries — the most serious to his left knee — during his 17-year NBA career, slipped away from the ball before going down near the Warriors' bench. Players and coaches stood over O'Neal as he lay in pain for at least a minute.
O'Neal was unable to put pressure on his right leg while being helped to the locker room by teammates Draymond Green and Ognjen Kuzmic, a 7-foot rookie from Bosnia and Herzegovina who will likely be counted on more if O'Neal misses any significant time. Fellow reserve center Festus Ezeli, who appeared in 78 games (41 starts) as a rookie last season, is working back from right knee surgery and will likely be out until at least February.
It was the second straight night the depleted Jazz pushed a Western Conference contender, a small sign of progress in a season that has had little. Utah lost its first eight games this season before beating New Orleans this week.