The win was the Pistons' eighth in the last 10 meetings.
Kobe Bryant scored 29 points for the Lakers, but went 12-of-30 from the floor.
"We just played a good all-around game," Iverson said after the Pistons won for the third time since his arrival from Denver five games ago. "It's just about playing basketball, understanding what we want to do on the basketball court.
"We didn't feel like it would take long, but we knew it would be kind of shaky in the beginning because I'm a totally different player than Chauncey Billups. I'm a lot more aggressive when it comes to driving to the basket, so my teammates have to know what spot I want them to be in to be able to create shots for them."
In winning their first seven, the Lakers had averaged a league-high 104.7 points and held opponents to a league-low 86.7.
The Pistons obviously beat them on both ends of the court, with Los Angeles becoming the final NBA team to lose this season.
"We just played defense," Iverson said. "We made them take tough, contested shots. When they missed, we got out and ran and took advantage. On the offensive end, we just attacked all night."
Bryant said the Pistons presented a "matchup issue" for the Lakers' defense.
"With Rasheed Wallace at the 5, and his ability to stretch the floor, it opened up the lanes for the guards," Bryant said. "We didn't shoot particularly well, but those guys were hot, too, in the first half and third quarter and kept us at bay.
"They're one of the top teams in the Eastern Conference, obviously. And they caught us on a night when they were hot as a pistol and we were pretty cold."
The Pistons shot 51 percent and the Lakers 42 percent. Wallace, the Pistons' center, went 4-of-9 from 3-point range.
Detroit usually plays rugged defense against Bryant, who had 17 points through the first three quarters as the Pistons took command. They have held him to 20 or fewer points in five of the last nine meetings.
The Pistons beat the Lakers in Los Angeles despite playing back-to-back games -- Detroit won at Golden State the previous night.
Both Bryant and Iverson moved up on the NBA's career scoring list. Bryant has 21,817 points and jumped into 21st ahead of Larry Bird (21,791) and Gary Payton (21,813). Iverson (23,156) passed Elgin Baylor (23,149) to jump to No. 19.
Brown was booed often, but afterward he smiled and said, "They booed me when I was here."
The Pistons moved in front to stay late in the first quarter, and held a double-digit lead for most of the second half.
Detroit stretched the lead to 77-62 on Arron Afflalo's 3-pointer in the closing seconds of the third period. The Lakers pulled to 61-56 earlier in the quarter, but Prince made a reverse dunk and sank two free throws to help the Pistons stay in control.
Bryant, in his 13th season, was playing in his 874th game. Bird played in 897 games over his 13-year career. ... Iverson, who averaged 17 points in two losses in his first games with Detroit, scored 30 in a win over Sacramento and had 23 points and nine assists in a 107-102 win at Golden State on Thursday night. ... He had faced the Lakers once already this season, scoring 13 points on 3-for-8 shooting in a 104-97 loss, his final game for Denver.