Sweden's Marcus Berg opened the scoring before skipper Ibrahimovic, who plays for French Ligue 1 club side Paris Saint-Germain, netted twice in four minutes just before half-time, with Dejan Damjanovic hitting a penalty consolation for the away side.
Berg told Swedish broadcaster Kanal 5: "It was very important that we got the 1-0. It meant we could relax and play. It was a perfect pass from Albin [fellow Swedish player Albin Ekdal] and a great shot from me."
"We killed the game in the first half," he added.
But there was bad news for Sweden's Kim Källström who was given a yellow card, which means he will be unable to play in his side's next qualifying game against Russia on September 5th. The player only recently left Russian side Spartak Moskva to join the Swiss Grasshoppers.
Elsewhere on Sunday, reigning European champions Spain closed in on a place at Euro 2016 by grinding out a 1-0 qualifying win over Belarus on Sunday and a late goal from Wayne Rooney's late goal gave England victory in Slovenia.
Estonia defeated minnows San Marino -- England's next opponents in September -- 2-0 in Tallinn.
Russia were the day's big losers, a defeat to Austria coming as a blow to their prospects of reaching the finals in France in a year's time.
Tens of thousands of thousands of fans from around Europe are expected to flock to French cities in 2016 with games being staged in stadiums across the country from Paris to Marseille and Bordeaux to Lille.
Meanwhile Sweden's women are continuing their campaign in the Fifa Women's World Cup in Canada.
After a 3-3 opener against Nigeria
and a 0-0 draw with the USA
on Friday, the team take on Australia in their third Group D match on Tuesday.