Johannsson on target but injured as AZ edge Vitesse
He then added a second late in the first half when skilfully chipping opposing keeper Piet Velthuizen from 18 yards.
Johannsson, who has now scored 13 league goals this campaign, was forced at half-time because of a thigh injury.
The victory saw Alkmaar move up to sixth on the Dutch table, 11 points from leaders Ajax.
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