Solskjaer's men drew 2-2 with Stromsgodset while Rosenborg - the only side who could stop them - were thrashed 6-3 at home by Brann.
The results gave Molde an eight-point advantage at the top with just two rounds to go.
Molde almost threw away the chance to end the title race today when they conceded a last-minute equaliser to Stromsgodset's Anders Konradsen.
But Rosenborg, kicking-off later, buckled under the pressure as Brann ran riot - Rudolph Austin and Birkir Mar Saevarsson scoring twice to stun the home crowd in Trondheim.
"The club has waited 100 years for this," former Manchester United striker Solskjaer told VG afterwards.
"We have been close several times so this was well deserved.
"When Brann went 4-1 I realised we had done it.
"It was a good atmosphere in the dressing room and we will enjoy ourselves tonight."