Sergei Bobrovsky made 22 saves in the second straight shutout victory for the fifth-seeded Russians, who earned a meeting with Finland in the quarterfinals Wednesday.
Ilya Kovalchuk and Alexey Tereshenko also scored, but the Russians had to survive another difficult game in Sochi. They failed to earn a bye to the quarterfinals after being forced into two shootouts in the preliminary round, losing to T.J. Oshie and the U.S.
The powerful Russian lineup struggled early against winless Norway, but Radulov's soft backhand finally beat Lars Haugen early in the second period, ending Russia's scoreless streak of more than 101 minutes.
Kovalchuk scored late in the second period, and Russia abruptly doubled its margin of victory in a tight game with two late goals. Radulov got an empty-net goal with 1:07 to play, and Tereshenko added another score in the final minute.
Haugen stopped 27 shots for Norway, which has never beaten Russia in a major tournament.
Russia's strength in Sochi has been its goaltending, and coach Zinetula Bilyaletdinov continued to rotate his netminders after Semyon Varlamov shut out Slovakia two days ago. Bobrovsky played well in the Russians' loss to the U.S., but yielded four goals to Oshie in the shootout.
With Bobrovsky's blanking of Norway, Russia hasn't allowed a goal in 140 minutes, 33 seconds.
Norway hasn't won an Olympic hockey match since its home Lillehammer Games in 1994, and the team finished last in group play in Sochi with three losses of declining quality. The Norwegians also faced Russia without Mats Zuccarello, its only NHL player. The New York Rangers forward watched from a suite with a bandage visible on his left hand.
But this imperfect, top-heavy Russian team faces incalculable pressure in Sochi, with everyone from President Vladimir Putin on down eagerly anticipating a medal run in the nation's first home Winter Olympics.
Even a meeting with Norway was a nail-biter, and Finland presents a formidable challenge with its veteran-laden roster and strong defensive play.
After Bobrovsky was forced to make several tough saves in a scoreless first period, Radulov got the Russians' first goal in more than 101 minutes. The oft-criticized forward circled the net and flung a backhand at the feet of Haugen, who probably should have stopped it. Radulov pumped his fists and screamed as the Bolshoy Ice Dome crowd let loose a cathartic roar.
Late in the period, Radulov drove the net put a shot off Haugen's post. Kovalchuk swatted home the rebound off the back of Haugen's leg.
Russia's offensive drought includes stars Alex Ovechkin and Evgeni Malkin. Ovechkin had a goal and an assist in the opening minutes of Russia's Olympic opener against Slovenia, but the reigning NHL MVP hadn't scored since. Malkin also hasn't scored a goal since the first period of the Russians' opener.