The local hero took only seven minutes to break the deadlock when the Milan striker held off a challenge and controlled a Kim Kallstrom cross from deep on the left before calmly firing home past Aldo Simoncini.
Five minutes later the game was effectively over as a contest as another Simoncini, defender Davide, turned Sebastian Larsson's low cross into his own net with Ibrahimovic lurking behind him.
Sweden attacked relentlessly and another deep ball into the box from Kallstrom paved the way for the third goal. Pontus Wernbloom, who scored twice on Friday against Hungary, rose to challenge the goalkeeper, the ball bounced off the pair and rolled into the net.
Olympiakos defender Olof Mellberg was then shown a red card for a reckless challenge in the 34th minute and will now miss the qualifier against the Netherlands on October 12.
Sweden coach Erik Hamrén replaced Ola Toivonen with Andreas Granqvist at half-time to restore the balance at the back and he repaid the trainer by powering home a header from Sebastian Larsson's free-kick to put Sweden 4-0 ahead.
In the 77th minute Ibrahimovic struck again, drifting in from the left and hammering a right-footed shot low to the goalkeeper's right. Five minutes later he was substituted to raucous applause from the home crowd to be replaced by Marcus Berg.
PSV Eindhoven striker Berg then had a toe-poke cleared off the line before he finally snatched a sixth for Sweden in the 93rd minute, heading home from close range.
"It felt fantastic. We played in my hometown, we managed to score six goals, it doesn't get any better than this," a delighted Ibrahimovic told Swedish television. "The fans showed what I meant to them, and I tried to give back as much as I could."
