Rosenborg and Molde began the day in a three-way points tie at the top of the table with Stromsgodset, who won 3-2 at Haugesund on Friday.
The first half was a tense affair with the best chance falling to Rosenborg's Swedish left back Mikael Dorsin who dribbled his way past the Molde defence only to shoot straight at the goalkeeper just before halftime.
Another Swede Rade Prica passed up a gilt-edged chance at the start of the second half when he failed to steer home a dangerous cross from the left.
Molde then began a period of sustained pressure that led to Pape Pate Diouf heading home Mattias Mostrom's corner on the hour mark to open the scoring.
Rosenborg brought on veteran striker Steffen Iversen as they battled desperately to get back into the game.
With Rosenborg's goalkeeper Daniel Orlund joining the attack for an injury time corner, Molde's Etzaz Hussain put the game beyond reach when he fired into an empty net to provoke wild celebrations from manager Ole Gunnar Solskjaer.
At the other end of the table, Stabaek were relegated following a 1-0 loss to Viking Stavanger. The club, from the Baerum suburb of Oslo, have amassed only 14 points in the their 27 games to date and are ten adrift of second-to-last Fredrikstad.
The top four face each other next weekend, when leaders Molde visit fourth-placed Tromso and Rosenborg travel to Stromsgodset.