Gortat struck for 18 points and corralled 13 rebounds for the Wizards, who broke a three-game skid.
John Wall helped out with 17 points and eight assists.
The Wizards broke open a close game with a 17-0 surge during a 6-minute span in the third quarter.
The Bobcats got 27 points from Gerald Henderson but couldn't avoid a sixth loss in seven games.
Kemba Walker added 19 for Charlotte.