Irving went 11-of-20 from the field with a trio of 3-pointers. Varejao added nine points, nine assists and two blocked shots for the Cavaliers, who outrebounded Washington 54-39.
First-round draft pick Dion Waiters marked his NBA debut with 17 points and three steals for Cleveland. Tristan Thompson notched a double-double with 12 points and 10 rebounds for the Cavs.
Jordan Crawford led the Wizards with 11 points despite going 0-for-6 from 3-point range.
Emeka Okafor added 10 points, seven rebounds and four blocked shots for Washington.