The Irish host the Swedes in a vital World Cup qualifier next month and keeping the Paris St Germain frontman, who famously scored four against England last year, quiet will be their prime concern.
Ibrahimovic struck twice in the first half hour at the Friends Arena but Norway were level at the break after a Mohammed Abdellaoue penalty and a Stefan Johansen effort.
Ibrahimovic soon restored the advantage, though, and Anders Svensson wrapped up the win.
Liverpool forward Luis Suarez showed he remains in good touch despite the persistent speculation over his future with an influential display in Uruguay's 4-2 win in Japan.
Suarez set up Diego Forlan's opener, won the free-kick for his strike partner's second and then added the third.
Manchester United's Shinji Kagawa cut the deficit but Alvaro Gonzalez grabbed Uruguay's fourth before Keisuke Honda struck a Japan consolation.
Mirko Vucinic struck the equaliser as Montenegro, England's chief rivals for a World Cup spot, drew 1-1 in Belarus.
Ukraine, who host England in Kiev next month, were 2-0 winners over Israel thanks to goals from Ruslan Rotan and Yevhen Seleznyov.
Wigan's Jean Beausejour and Barcelona forward Alexis Sanchez scored two goals apiece as Chile thrashed Iraq 6-0 in their friendly in Brondby, Denmark.
Manchester City striker Edin Dzeko continued his good pre-season form with two goals for Bosnia-Herzegovina but it was not enough to prevent a 4-3 loss to the United States in Sarajevo.
Dzeko and Vedad Ibisevic put Bosnia in command but a hat-trick from new Sunderland signing Jozy Altidore after Eddie Johnson pulled one back turned the game around. Dzeko's second came in the last minute.
Germany recovered from the shock of conceding twice in the opening 14 minutes to draw 3-3 with Paraguay at Kaiserslautern.
Ariel Nunez and Wilson Pittoni were on target early for the visitors but Ilkay Gundogan and Thomas Muller levelled. Miguel Samudio put Paraguay back ahead but Lars Bender secured a draw.
Argentina beat Italy 2-1 in Rome after goals from new Napoli signing Gonzalo Higuain and Ever Banega. Lorenzo Insigne replied for Italy.
Switzerland produced the shock of the night as they ended Brazil's 11-match unbeaten run with a 1-0 win in Basel.
Dani Alves headed into his own net in the first half to gift the Swiss, who are in a strong position in the race to qualify for the World Cup in Brazil, victory.
Cristiano Ronaldo scored an 87th-minute equaliser as Portugal drew 1-1 with Holland in Faro. Kevin Strootman had put the Dutch ahead after 17 minutes.
Portugal will doubtless have been cheered by the news Russia had missed a chance to move above them in their qualifying group by losing in Northern Ireland.
They may be wary however that the next match in their campaign is in Belfast next month.
Belgium, who face Scotland in Glasgow next, played out a goalless draw with France in Brussels.
Macedonia, who play Wales in September and Scotland the following month, beat Bulgaria 2-0 in Skopje with late goals from Agim Ibraimi and Aleksandar Trajkovski.
Another of England's upcoming opponents, Moldova, drew 1-1 with Andorra after an equaliser from Alexandru Dedov.
Manchester City's new striker Alvaro Negredo and Santi Cazorla of Arsenal were on target as world and European champions Spain won 2-0 in Ecuador.
The match was halted in the 11th minute in tribute to Christian Benitez, the Ecuador international and former Birmingham City player who died last month.
Benitez wore number 11 for his national team and a standing ovation was observed as the game was interrupted in his honour.
Negredo was set up for the 25th-minute opener by his new City team-mate David Silva who, along with Andres Iniesta, had already hit the post.
The second from Cazorla came just after the hour.