VanVleet also had six assists.
After grabbing a defensive rebound, veteran Vanfleet crossed the field and his big shot gave Toronto a 105-97 lead, with 2:28 on the clock.
After Spencer Dinwiddie missed a long-range shot, one VanVleet free throw and two Khem Birch free throws brought the Raptors to their destination.
For the first time in their history, the Raptors (6-3) won their first four games abroad.
OG Anunoby scored 21 points and three shots, bolstered by 15 points each for Svi Mykhailiuk and Gary Trent.
Valuable Achewa scored 10 rebounds and struck a heavy blow, allowing the visitors to finish the third quarter ahead 86-77.
The inning ended with the Raptors leading 59-48, after Trent picked up a basket at the last second (and a free throw).
In the last quarter, the Raptors helped their cause with an 8-0 push, as they advanced 101-86. Anonobi capped this push with a three-point shot.
Scotty Barnes missed the second game in a row due to a sprained right thumb.
The Raptors will meet their home fans Friday night, against the Cleveland Cavaliers.
Bradley Bell scored 25 points for the undefeated Wizards in three home games.
