The Pistons had a chance to win after a timeout with 5.1 seconds left, but Billups missed a 3-pointer just before the buzzer.
Mehmet Okur had 10 of his 22 points in the fourth quarter to help Utah improve to 4-0 over the last two seasons against his former team and to end a four-game losing streak.
"We always seem to play well against the Pistons," Williams said. "But this one was important to stop the bleeding."
Webber, who signed the previous day, was with the team for only the morning shootaround before entering the game with 10:07 left in the first half and was welcomed by a standing ovation. The five-time All-Star made his first shot before missing his next four and finished with two points, five rebounds and three assists over 17 minutes in his first game since Dec. 27.
Philadelphia bought out the final 1 1/2 years of his contract last week.
Clearly, Webber was not discouraged by the result of his first game playing with his hometown team.
"I'm sure people expected more, but you can't judge this on one night," he said. "I'm telling you, this is going to be special."
His new teammates agree.
"He had limited mobility, but he played great and carried us at times in the first half," said Tayshaun Prince, who scored 17. "It's going to take some time for us to get a feel for him and vice versa."
Billups had 26 points and seven assists in 35 minutes after missing the previous eight games with a calf injury.
"I've been working at not letting it affect me too much," he said. "I felt good."
The Pistons were 3-5 without the All-Star guard in the lineup and have lost eight of their last 11 games overall.
"It seems right now our confidence is shaky," Detroit coach Flip Saunders said. "When things have gone bad, we've settled for jumpers and we've lost some of our aggressiveness."
Rasheed Wallace, who had 11 points, was called for a technical while Williams was shooting free throws. That allowed Okur to shoot a free throw to give the Jazz a seven-point lead with five minutes left, and the point proved to be the difference in the closely contested game.
Saunders appeared to be upset with Wallace, shouting at him from the sideline, but it was too late.
Detroit's Antonio McDyess scored 16 points, matching his season high for the second straight game, and fellow reserve Lindsey Hunter had 12 points in his second straight game after returning to the lineup Monday from an injury.
The Pistons got off to an awful start, missing their first seven shots, but trailed just 26-24 after the first quarter. Detroit went ahead 51-46 at halftime before falling behind 72-70 entering the final quarter.
Okur made his sixth straight shot midway through the fourth quarter to put the Jazz ahead by seven points. Each time Detroit rallied, he or Williams made shots or free throws to keep Utah ahead of the Eastern Conference power it has dominated lately.
"We like the challenge," Okur said. "We always play good against good teams."
Williams, in his second NBA season, had his best performance offensively after shooting poorly recently.
"I never felt like I was off track. I just wasn't getting shots to fall," he said. "I knew I was playing well and doing everything I was supposed to do. Sometimes that just happens."
Williams' previous career high was 28 points, a total he reached for a third time on Jan. 6. ... Webber, who can't be No. 4 because it's retired by Hall of Famer and president of basketball operations Joe Dumars, is wearing No. 84 because his nephew dreamed that would be his uncle's new jersey number. ... Okur is in his third season with the Jazz after being drafted by the Pistons, who couldn't re-sign him and Wallace after winning the 2004 NBA title. ... Detroit C Nazr Mohammed, who essentially has asked for a trade, did not play for the first time this season.