Butler scored 18 points to go with 10 rebounds and 10 assists. Wade added 20 points, 10 assists, and nine rebounds with a potential 10th board ripped out of his hands by a teammate in the closing seconds.
The Bulls have won four straight and defeated the Cavs in all three games this season.
Kyrie Irving led all scorers with 34 points. He nearly had a triple-double too, finishing with a season-high nine rebounds and seven assists. Kyle Korver and James Jones each scored 14 points off the bench for the Cavs.
Cleveland is 0-4 this season without James, who missed the game because of illness, and has lost its last seven games when he doesn't play. Dating to the start of the 2014 season, the Cavs are now 4-19 without him.
Korver owns the fifth-most 3-pointers in NBA history, passing Vince Carter (2,011 3s) and Jamal Crawford (2,013 3s) with four treys. He fell awkwardly with 2:59 remaining in the game and limped off the court toward the locker room.
Cameron Payne (six points) and Joffrey Lauvergne (two minutes) made their Chicago debuts. On Thursday, the Bulls traded popular veteran Taj Gibson, Doug McDermott and a 2018 second-round pick to the Oklahoma City Thunder for Payne, Lauvergne and Anthony Morrow.
The Bulls had seven players score in double figures. Rajon Rondo was among them with 15 points off the bench. Fellow reserve Nikola Mirotic added 14 points and 10 boards.
Irving has scored at least 20 points in eight consecutive games.
NOTES: Free agent point guard Deron Williams cleared waivers and will sign with the Cavs for the remainder of the season. Williams is close friends with Cavs G Kyle Korver, and they share the same agent, Jeff Schwartz. ... Bulls G Michael Carter-Williams (patellar tendonitis) didn't play Saturday night or make the trip to Cleveland. Chicago coach Fred Hoiberg said there was no timetable for Carter-Williams' return. He played just eight minutes in Friday's win over Phoenix. ... Counting F LeBron James, the Cavs were missing three starters from their championship team. G J.R. Smith (thumb surgery) and F Kevin Love (knee surgery) also didn't play against the Bulls.