David Healy followed his hat-trick against Liechtenstein on Saturday with two more goals at Windsor Park to knock the Swedes out of first place in the race to reach the finals in Austria and Switzerland.
The Leeds striker, who has now scored 29 goals in 58 international appearances, equalised Johan Elmander’s opener before grabbing a second half winner that put Lawrie Sanchez’s side in pole position in a qualifying group for the first time since 1988.
Healy served notice of his threat to the Sweden defence after just two minutes as he met Damien Johnson’s cross with a shot that hit the side-netting.
Sweden, who had won their previous four qualifiers to head the group, made a cautious start, but they almost went in front when Zlatan Ibrahimovic shot narrowly wide in the 24th minute.
Sanchez’s team were equally close a minute later when Michael Duff headed just over the bar following a corner from Chris Brunt.
But Sweden opened the scoring in the 27th minute with a fine counter-attack. After a probing spell of possession, Niclas Alexandersson’s knock back teed up Elmander and the striker drove home from close range.
That setback only served to redouble the hosts’ efforts and they were level four minutes later.
Healy, who struggles to hold down a place in Dennis Wise’s Leeds team, has been in superb form for his country and he produced a fine equaliser.
He found space between two defenders to send a superb volley over the head of Andreas Isaksson for his eighth goal of the qualifying campaign.
Sweden nearly reclaimed the lead soon after half time when Ibrahimovic’s effort was scrambled off the line by Grant McCann.
Just as the visitors looked set to exert a spell of pressure, Northern Ireland stole the lead.
Sanchez had brought out the best in Healy and the forward made it 21 goals in 27 matches under the former Wycombe manager in the 58th minute.
Northern Ireland have become a tough nut to crack under Sanchez and they refused to surrender their lead, leaving Sweden to join England and Spain as the latest famous scalp for the hosts.