While coach Erik Hamren will be concerned about conceding two soft goals, he could not fail to be impressed by AC Milan forward Ibrahimovic.
Having orchestrated a 3-1 win against Croatia in February, Ibrahimovic was deployed in a free role again against Iceland and volleyed the opener from the edge of the box after two minutes.
His economic use of the ball, flicking first-touch passes off either foot, encouraged the home side to a style of play more Spanish "tiki-taka" than Scandinavian pragmatism.
In the 14th minute he created Sweden's second goal, chasing down a loose ball before bamboozling a defender and crossing for Ola Toivonen to tap home from close range.
Two goals to the good early on, Sweden looked like they were preparing for a rout but the coach in the away team's dugout had a point to prove.
Lagerback's influence was clear to see, however, with Iceland's diligence getting them back in the game when Kolbeinn Sigthorsson beat Olof Mellberg to reduce the deficit just before the half-hour mark.
The slew of half-time substitutions slowed the game down, with the exception of Sweden's Pontus Wernbloom, who mixed his usual quota of tough tackles with some sprayed passes.
Wilhelmsson's sleight of foot on the wing ensured Ibrahimovic was not missed, and his efforts were rewarded when he volleyed Sweden's third in the 78th minute.
