The four-time NBA Defensive Player of the Year left the Detroit Pistons for a four-year, $60 million free agent deal with the Bulls in the offseason. Wallace, not known for his shooting, missed everything on his first free throw attempt and finished 1-for-6 from the line.
Luol Deng scored 13 points and Kirk Hinrich added 11 for the Bulls in their preseason opener.
The Bulls were trailing 86-82 with 1:37 left in the game when Andre Barrett made two free throws to cut the lead to two. Chicago's Michael Sweetney made one free throw to make it 86-85 with 1:26 left, and Barrett put Chicago ahead with a jumper with 17 seconds left.
Roger Mason Jr. missed a jumper for Washington (0-2) with 2 seconds left.
Antonio Daniels scored 13 points and Gilbert Arenas added 11 in 14 minutes for Washington.
Tyrus Thomas, the No. 4 overall pick in this year's draft, played 16 minutes and scored six points on 2-of-7 shooting for Chicago.
Arenas played only the first seven minutes in the opening half and scored seven points as Washington took a 45-41 lead.
Caron Butler dressed for the Wizards, but was given the night off by coach Eddie Jordan.
Donell Taylor finished with 12 points and Jarvis Hayes scored 11 for the Wizards.