Neither side managed a point over the final 2:30 and Nene ultimately clinched the victory by blocking a 3-point attempt by Jimmy Butler just before the buzzer.
The Wizards won their third in a row to climb to the .500 mark.
Washington shot 51 percent from the field with John Wall leading the way by scoring 24 points and dealing out 10 assists. Bradley Beal added 14 points for the Wizards, while both Gortat and Martell Webster had 13.
Notable deaths of 2014 [PHOTOS]
Arizona Cardinals player formally charged