Kirk Hinrich added 18 points and Nazr Mohammed had a season-high 17 for the Bulls, who will face the Brooklyn Nets in the opening round of the playoffs.
It sure wasn't easy.
A.J. Price scored a career-high 24 points and John Wall overcame a slow start to finish with 23 for the Wizards, who kept coming back every time it looked as though the Bulls were ready to put them away.
Chicago led by 21 late in the first quarter but allowed Washington to pull within a point in the second. Chicago then got the lead back up to 11 in the third, but the Wizards rallied again.
This time, Washington tied it at 85 on a 3-pointer by Price with just over three minutes left before the Bulls responded with seven unanswered points. Richard Hamilton fed Jimmy Butler for an alley-oop dunk, Hinrich hit a floater and Luol Deng nailed a 3 - after missing five of his first six field goal attempts - to make it 92-85 with 1:42 remaining.
The Wizards cut it to 94-92 on a 3-pointer by Wall and a floater by Price with 26.1 seconds left. Hinrich then had a chance to make it a two-possession game but missed the first free throw before hitting the second to make it 95-92 with 17.1 seconds left.
Taj Gibson blocked a 3-point attempt from the wing by Price with 10 seconds left, and Wall put up an air ball from long range at the buzzer with Butler guarding him, preserving the win for Chicago.
It was a difficult finish to a difficult regular season for the Bulls.
They battled a long list of injuries, topped by former MVP Derrick Rose's season-long recovery from surgery to repair a torn anterior cruciate ligament in his left knee.
Just about every other key player has been banged up at some point, and Joakim Noah (foot) and Taj Gibson (knee) had their minutes limited in this one.
The Wizards had their share of injuries, too, and a season that started with 12 straight losses ended with them dropping their sixth in a row. They were missing Emeka Okafor after he sprained his right ankle against Brooklyn on Monday.
Notes: Besides Okafor, Washington was also missing Bradley Beal (stress injury, right fibula), Nene (sore left foot), Martell Webster (strained abdomen), Trevor Ariza (sore left knee) and Leandro Barbosa (torn left ACL).