Millsap had 30 points and 16 rebounds, Jefferson added 23 points and 10 rebounds and Williams directed the show before finishing with 16 points and 15 assists as Utah broke into the win column after an 0-2 start.
"People said a lot about our team, but tonight we proved otherwise," Millsap said. "We proved that we could play defense, we proved that we could move the ball like we're supposed to, we proved that we can make shots."
The Jazz haven't started 0-3 since the 1979-80 season, when they lost four in a row and 17 of 19 in the franchise's first year in Utah.
Instead, they snapped Oklahoma City's season opening two-game win streak behind a strong push in the middle of the game when they outscored the Thunder 40-13.
"We knew we could play a lot better offensively and defensively. That's why I said we weren't worried," Williams said. "Upset because we're losing, but we weren't worried.
"We knew we could play a lot better on both ends. We came out and did that."
Kevin Durant led Oklahoma City with 28 points but also had six of the team's 14 turnovers. Russell Westbrook scored 22 to go with four steals. That wasn't nearly enough to contain Williams, who got Utah's offense clicking for 32 assists on 44 made baskets.
With Williams directing the way, the Jazz started pulling away with a 17-4 run to finish the first half. He set up C.J. Miles and Jefferson for two-handed jams before hitting his own short jumper in the lane.
Thunder coach Scott Brooks finally pulled Westbrook out of the game and replaced him with Eric Maynor, only for Williams to go after him. Williams isolated against Maynor and dribbled into the lane, then kicked it out for his 10th assist of the first half on Miles' 3-pointer from the left wing.
"We just [weren't] playing tough enough," Westbrook said. "We couldn't get a stop and they were executing their plays very well."
Utah finished off its first-half flourish when Andrei Kirilenko curled into the lane for a basket and converted it into a three-point play and a 56-40 halftime lead.
And the Jazz weren't done yet.
Kirilenko made a 3 to start a 17-6 run to open the second half for Utah, pushing the lead to 73-46 before Oklahoma City made its big charge. The Thunder startled Utah with a full-court press, converting a series of turnovers into an 11-0 comeback.
Oklahoma City was never able to get closer than 98-85 after Westbrook drove for layups on back-to-back possessions early in the fourth quarter.
"It was a team effort, and as a team we didn't come ready to play," Westbrook said.
Jefferson converted a three-point play off a third-chance basket and Miles added another 3 during an 8-0 run that made it 112-90 and convinced Brooks to send his reserves into the game with just under 5 minutes to play.
"We feel so good that finally we got the first win," said Kirilenko, who scored 19 and helped hold Durant to only nine by the time the Jazz were up by 27. "We had a great preseason, but the last couple games, we're supposed to lose. That's not the way we're supposed to play.
"Tonight, finally we found that rhythm offensively and defensively. So, I hope we can stay that way."
Miles finished with 21 points off the bench, breaking through after he was 1-for-8 in two foul-plagued games to start the season.
"When we play hard from top to bottom, from start to finish, everybody's in a rhythm because everybody's in the game," Miles said.
Utah lost Jeremy Evans to a sprained right wrist in the first quarter. ... Cole Aldrich had an electrifying debut for the Thunder. The No. 11 pick in this year's draft charged in and slammed home James Harden's missed shot with 1:01 left in the first quarter for his first points in the NBA. ... The only times the Jazz started 0-3 or worse were their first NBA season in New Orleans (1974-75) and their first in Utah (1979-80). ... Oklahoma City's mascot, Rumble, led three kids in some courtside trick-or-treating during a second quarter timeout skit, then stole all of their candy -- until referee John Goble knocked the bison down with a screen and pinned him with his foot.