Earlier, Christian Eriksen gave Ajax the lead in the 21st minute before Roy Beerens levelled on the stroke of half-time. Siem de Jong edged Ajax ahead 15 minutes into the second half prior to Johannsson's penalty before Viktor Elm won it for Alkmaar in the 74th minute.
The goal adds to Johannsson's season opener in the 4-2 loss to Heerenveen last week. He is due to link up with the USA national team for the first time in Bosnia this week.
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