After a goalless first half, Norway took the lead through Antonio Nusa in the 59th minute.
Erling Braut Haaland then played in Andreas Schjelderup, who made it 2-0 from close range.
Wales certainly brought the game to life with its penalty, but Haaland secured the win by converting from the spot to make it 3-1.
The result means Norway will remain in Nations League A and could also advance to the quarter-finals. On Tuesday, Norway faces Denmark in a heated Nordic encounter.
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