The Barcelona man, who only announced his return to the national side last month, wasted no time in getting on the scoresheet as he put the Swedes ahead with a simple tap in after just three minutes.
Emir Bajrami got his first international goal when he sent a superb strike past Allan McGregor at the second attempt to double the lead five minutes from the break.
Ola Toivonen headed in the third ten minutes after half-time in controversial circumstances after the ball appeared to go out for a goal-kick before substitute Kim Källstrom sent in his cross.
Sweden dominated the game against an under strength Scotland side, that was
hit by a raft of call-offs prior to the match, to condemn manager Craig Levein to his first defeat in only his second game in charge.
McGregor was handed his first start in 17 months after his lifetime ban from the Scottish Football Association was overturned and he found himself picking the ball out of the net in the fourth minute.
A slick pass found Bajrami in space on the right wing and his low cross was sidefooted home by Swedish captain Ibrahimovic who was unmarked eight yards
The Barcelona star was pulling all the strings for Sweden and only a lunging clearance from Christophe Berra stopped his floated pass finding Bajrami in the box.
McGregor was kept busy on his return to international duty. The Rangers keeper spilled a Toivonen drive from outside the box but he redeemed himself when he got out quickly to bravely block Johan Elmander’s fiercely struck close-range follow-up.
Swedish stopper Andreas Isaksson was a spectator until the half-hour mark when he nearly gifted Scotland an equaliser.
The ‘keeper dropped James McFadden’s cross from the left but he managed to recover in time to block from Blackpool midfielder Charlie Adam as he tried to
knock it past him.
Bajrami scored a sensational second in the 40th minute. The FC Twente forward controlled Anders Svensson’s chipped pass on his chest before unleashing a fierce left-foot strike which McGregor saved well but the rebound fell to his right foot and he steered into the far top-hand corner.
Sweden continued to threaten the Scots goal after the break and Toivonen made it 3-0 in the 56th minute with a controversial goal.
The Scotland defence seemed to switch off when the ball looked to have gone out for a goal-kick but Källstrom cut it back for the PSV Eindhoven forward, who rose unmarked to head it past McGregor.
Middlesbrough striker Kris Boyd replaced Steven Fletcher in the 65th minute and almost scored immediately when his volley on the turn was stopped by the outstretched leg of Isaksson after he connected with Darren Fletcher’s chipped pass.
Sweden could have made it four with ten minutes to go when Toivonen got on the end of a fast break and only a superb one-handed save from McGregor in the besieged Scotland goal denied him.
Scotland sub Chris Iwelumo picked out Boyd in the box with a neat pass late on but he sliced his effort over.