The USA international's 29th-minute penalty gave the Dutch side a narrow lead in the first leg of the Round of 16 in Europe's secondary club competition which concluded in Russia next week.
23-year old Johannsson's well-struck spot-kick saw Anzhi keeper Mikhail Kerzhakov get a hand to the ball but there was enough force to give AZ a first-half lead which they hung onto for the remainder of the contest.
The goal was Johannsson's 25th in all competitions this season, making him just the second American to reach the achievement, following on from former AZ ace Jozy Altidore who fired home 31 goals last campaign prior to his move to Sunderland.
Johannsson has 16 Eredvisie goals to his name, as well as six in the KNVB Beker (Dutch Cup), one in the Dutch Super Cup and now two in Europe.
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