The tournament in Russia will be Panama's first appearance at world football's showpiece event, but it heads into it having only won one of its last seven matches.
Joshua King's strike – his second in as many games this month – was the difference at the Ullevaal Stadion, the Bournemouth striker firing Norway ahead in the fourth minute, holding off two defenders before poking past Jaime Penedo.
Fidel Escobar went close to equalising for Panama with a free-kick that stung the palms of Sten Grytebust, while Penedo needed to be alert at the other end to deny Tore Reginiussen early in the second half.
Substitute Gabriel Torres wasted Panama's most promising second-half move as he dragged a shot wide from 12 yards, leaving the visitor without a goal in both friendly matches before heading to Russia.
Ola Kamara should have doubled Norway's lead late on but he inexplicably blazed over from close range after excellent work by Crystal Palace striker Alexander Sorloth.
Luckily it mattered little for Norway as they picked up a fourth successive win, but Panama coach Hernan Gomez will hope for much better in its World Cup opener with Belgium.