The American international heavily influenced proceedings despite leaving the match at halftime with an injury.
The win saw AZ move into a tie for the fifth spot in the league, while Vitesse missed a chance to move to the top of the table with leader Ajax not in action until Thursday.
The first goal saw Johannsson dash down the left side of the box and put in a cross toward the back post for his teammate. It didn't reach its intended target but was instead deflected into the back of the net by Patrick van Aanholt for an own goal.
Suspect defending gifted the Icelandic-American his second chance as well, with the two center backs colliding when trying to beat Johannsson to a long ball. Though the defenders eliminated each other, Johannsson still had work to do before hitting the ball past the keeper, who had come off his line, with his first touch.
The 23-year-old U.S. national team striker left the pitch at the break with what appeared to be an upper leg injury. A prognosis was not immediately available.
AZ and American fans alike will hope the injury worry turns out to be nothing serious, with today's goal being Johannsson's 13th in league play this season and 22nd across all competitions. It was also his sixth goal in the last 10 Eredivisie matches for AZ, which returns to action against Go Ahead Eagles on Saturday.