Another three-point play by Butler made it 66-52.
Chicago (11-16) led by 19 at the end of the period after Reggie Evans' dunk with less than a second left ended a 5½-minute field goal drought for the Nets (9-19).
Brooklyn couldn't get much closer in the fourth and was serenaded with a chorus of loud boos from the fans.
What once was viewed as a Christmas Day showdown between Eastern Conference contenders became a matchup of two of the NBA's biggest disappointments so far, as both teams have been plagued by injuries.
Deron Williams scored 18 points and Mizra Teletovic added 17 for the Nets, who have lost four straight.
The victory was Chicago's second straight, the first time since five consecutive wins from Nov. 8-18 that the Bulls had two in a row. Chicago is starting to get healthy with the return of guard Kirk Hinrich and Butler, both of whom started.
Hinrich spurred a 12-0 run midway through the second quarter that gave Chicago a 39-31 lead. Williams then scored seven straight to make it a one-point game. Chicago led 41-38 at the half before Butler took over.
While the Bulls got both guards back, they were still missing Luol Deng (Achilles) and Derrick Rose, who is sidelined for the season with a right knee injury.
Brooklyn has its own injury issues with center Brook Lopez lost for the season Friday to a broken right foot.
The two teams were wearing their Christmas short-sleeve jerseys that look straight out of a rec league game. Instead of numbers and a team name on the front, there was a big shiny logo. There are numbers on the sleeves, while the backs look more like a normal NBA jersey.
Both teams were also wearing striped socks to complete the outfit.
Notes: The Nets were still missing forward Andrei Kirilenko, who has been sidelined this season with a back injury. Nets coach Jason Kidd said before the game that his forward is making progress. ... Kidd always has loved playing on Christmas. "One of the biggest honors as a player and coach is to participate on Christmas," he said. "The world is watching so you can showcase your talent." ... These two teams met in the first round of the playoffs last season and the Bulls won in seven games. ... Chicago has won eight of the last 10 regular-season meetings.