Antawn Jamison added 21 points and eight rebounds for the Wizards, who last won a post-season game on May 8, 1988.
Larry Hughes chipped in with 21 points and seven rebounds.
Chicago still leads the best-of-seven Eastern Conference opening round series 2-1, with Game Four in Washington on Monday.
Washington reserve Etan Thomas led a strong bench performance by the Wizards with 20 points and nine rebounds. Thomas went eight-for-nin from the floor.
The Wizards broke open a tight contest with a 13-2 run late in the third quarter to pull away from the Bulls, who themselves scored a pair of impressive home wins at the start of the series.
The victories were their first in the playoffs since the end of the Michael Jordan era in 1998.
Tyson Chandler had 15 points and 10 rebounds to lead six Bulls in double-figures scoring, but Chicago could only shoot just 39 percent.
Antonio Davis added 13 points and hauled down 11 rebounds for the Bulls before fouling out in the fourth quarter. He was ejected from the game for arguing the call on his sixth foul.
In other playoff games, Jason Terry scored a season-high 32 points as the Dallas Mavericks rallied to edge the Rockets 97-93 in Houston to even up their best-of-seven Western Conference opening round series at 2-2..
Terry hit the deciding three-pointer with 26.9 seconds left and Michael Finley and Dirk Nowitzki both added 18 points as the Mavericks won their second straight game in the series in Houston after losing the first two at home.
The Mavs trailed by seven points in the fourth quarter, but held the Rockets to just 16 points in the final 12 minutes to tie the series between the Texas state rivals.
Nowitzki added seven rebounds and six assists for Dallas, while Jerry Stackhouse chipped in with 10 points and six rebounds.
Tracy McGrady led all scorers with 36 points.
Yao Ming added 20 points for the Rockets, but no other Houston player scored more than seven.
Game Five is in Dallas on Monday.
In Indianapolis, Paul Pierce had 30 points, seven rebounds and eight assists as the Boston Celtics routed the Indiana Pacers 110-79 in Eastern Conference opening round series play.
Despite playing without the suspended Antoine Walker, the Celtics dominated Game Four to tie the best-of-seven series 2-2.
Game Five is in Boston on Tuesday.
Ricky Davis added 15 points for the Celtics, as all five Boston starters scored in double-figures in the easy win.
Stephen Jackson scored 24 points to lead the Pacers, who suffered their most lopsided playoff loss.
They also shot a franchise playoff worst 26.9 percent from the floor.
Reggie Miller added 12 points for Indiana.
In Denver, Manu Ginobili had 32 points and nine rebounds as the San Antonio Spurs defeated the Nuggets 86-78.
Robert Horry added 13 points off the bench for the Spurs, who take a 2-1 lead in the best-of-seven Western Conference opening round series.
Tim Duncan added 11 points and 11 rebounds in just 26 minutes for the Spurs, who lost Game One in the series at home.
Tony Parker added 10 points for San Antonio.
Carmelo Anthony had 19 points for the Nuggets, who trailed 50-41 at the half.
Kenyon Martin added 18 points for Denver, while Marcus Camby scored 12 points and pulled down 14 rebounds.
Game Four is in Denver on Monday.