P.J. Washington had 25 points and Kelly Oubre Jr. added 20 for the Hornets, who've struggled with injuries all season and have not won since upsetting the defending NBA champion Golden State Warriors.
Washington shot 52.5% from the field, while holding the Hornets to 41.6%.
The game featured 14 lead changes before Hachimura gave the Wizards the lead for good with a three-point play in the waning seconds of the third quarter.
Kristaps Porzingis plays 31 minutes, shooting 6 for 14.
Washington came out strong in the final frame, pushing its lead to double digits behind Kuzma, who started to score with drives and short jumpers. Kuzma finished with nine points in the fourth quarter on 4-of-6 shooting.
Monte Morris sent fans streaming to the exits with 1:19 left when he scored on a drive to the basket to beat the shot clock to push the lead to 11.
Wizards: Bradley Beal missed his second straight game while in the NBA's health and safety protocols. ... Bench outscored the Hornets 50-27. ... Had a season-low five 3-pointers.
Hornets: All-Star LaMelo Ball (ankle) missed his 11th straight game with a sprained ankle. ... Gordon Hayward (shoulder) and Cody Martin (quad) also remain out for Charlotte.
Wizards: Host Dallas on Thursday night.
Hornets: Host Portland on Wednesday night.