The Jazz outscored the Kings 27-17 in the fourth quarter in winning their second road game in a row after dropping the previous six. Utah had lost nine of 12 overall since beating woeful Cleveland on Jan. 14.
"We've struggled on the road, so this was a very important win for us," said Williams, who has been bothered by a lingering sore wrist. "It's not a pretty win, but at least it's a win. I'm hoping this gets us back on track."
It appeared the Jazz might be headed for another loss when Sacramento led by six midway through the fourth quarter. Looking for a way to slow down Evans and Cousins, Jazz coach Jerry Sloan went to a zone defense and it worked well. The Kings scored only seven points in the final 6:36.
"We went to the zone to give them a little something different," Sloan said. "They are a big and long team with Cousins and [Samuel] Dalembert inside, and Evans can get to the basket really well. They still hurt us with some offensive rebounds, but the zone definitely slowed them down."
Still, the Kings had their chances to win or send the game into overtime in the final 20 seconds. Omri Casspi took an awkward 3-pointer in the closing seconds that was an airball and the Jazz secured the rebound and the victory.
"We ran a play to set up for Tyreke, but I got kind of open," Casspi said. "I just lost the ball on the way up. The ball slipped out of my hands."
After both Evans and Dalembert missed potential game-tying shots, Andrei Kirilenko converted a free throw for a 107-104 Jazz lead with 6.8 seconds left.
Cousins converted a three-point play to pull the Kings to 105-104 with 1:04 left. But he quickly committed his sixth foul at the other end of the court, and Kirilenko made a free throw for a two-point Jazz lead.
Although he played only 30 minutes and had foul problems early, Cousins still finished with his fourth 20-point effort in the past five games.
"Cousins is amazing. The sky is the limit for him," Jefferson said. "He's going to be something special."
Kirilenko made a fast-break layup and fell hard to floor with 1:55 to go. The basket put the Jazz ahead 103-101.
Trailing by seven after three quarters, the Jazz pulled even in the first 4 minutes of the fourth. A dunk by Jefferson followed by Earl Watson's fast-break layup tied the game at 81.
It was Evans and Cousins scoring regularly in the third to give the Kings an 87-80 lead. Evans frequently penetrated inside and had 13 points in the quarter. Cousins converted a three-point play with 1.7 seconds left and had 11 points and eight rebounds.
"I thought the turnovers killed us," Kings coach Paul Westphal said. "They killed us in the first half and they killed us in the second. We built a lead in the second half by taking care of the ball, and then turnovers popped up again down the stretch. That's a good team and you can't just give them those possessions like we did."
Evans made a twisting, driving, left-handed layup in traffic and added a free throw after being fouled. The three-point play put the Kings ahead 73-66 midway through the third quarter.
Casspi scored nine points for the Kings, who led 56-55 after a first half with numerous lead changes. Jefferson scored 14 points for the Jazz and Williams had 11 points and six assists.
Sloan has signed a one-year contract extension for the 2011-12 season, which will be his 24th as Utah's coach. ... Donte Greene had a four-point play in the second quarter, breaking a 43-all tie and igniting an 8-0 run for the Kings. ... Kirilenko was back in the Jazz starting lineup after missing the previous three games with a sprained left ankle.