The visitors took a surprising lead in the 25th minute when Magnus Blakstad fired an effort past Inter keeper Raffaele Dalle Vedove.
This goal inspired the hosts to get back into the game, which they did through Forte who tapped in from close range 12 minutes before half-time.
Inter dominated the early stages of the second-half but couldn't find an elusive goal to give them the lead as they spurned several chances.
The hosts weren't made to rue their missed chances, however, when they finally got the goal they deserved through 16-year-old striker Thomas Pedrabissi who shot from the edge of the box was good enough to creep past Jacob Storevik in the Rosenborg goal.
Nerazzurri sealed the win five minutes from time when Forte grabbed his second of the game firing past Storevik to ensure his side finished top of Group 5 with a game in hand.
Inter's final game will be against Liverpool in January and will determine whether the Reds can secure a place in the last 16 of the competition as one of the four best third place finishers.