Sergei Bobrovski stopped 22 shots for the shutout, while captain Pavel Datsyuk contributed three assists for the Russians, who will now face Finland on 19 February for a place in the semi-finals.
Russia is desperate to win gold on home ice after a disappointing showing in Vancouver four years ago, where they exited at the quarter-final stage.
Radulov, who had been blamed for costing Russia two powerplay goals against the USA, more than redeemed himself with two goals and an assist against the Norwegians in front of a crowd of 11,423 at the Bolshoi Ice Dome.
Fellow forwards Ilya Kovalchuk and Alexei Tereshenko also found the net for Russia.
“Do or die”
“It’s do or die right now. Everybody is ready for [the match against Finland],” said their team-mate Alex Ovechkin”
Ovechkin, widely regarded as Russia’s star forward, has yet to find scoring form in Sochi, but he says he is more than happy to see the goals coming from elsewhere in the team.
“The most important thing is the team,” he said. “It’s not about personal stats. We are here to win the gold. It’s not about winning some scoring titles.”
Earlier in the day, Slovenia defeated Austria, scoring three times in the first 24 minutes en route to a 4-0 win. The Olympic debutants will now face Sweden at the Shayba Arena on 19 February.
“Small Slovenia, playing in the quarterfinal of the Olympic Games?” said Slovenian goaltender Robert Kristan after completing a 30-save shutout. “Let's say it is a miracle because this is really amazing.”
Neighbours Czech Republic and Slovakia produced the highest scoring game of the day, an eight-goal thriller, which saw the Czechs prevail 5-3 to move into the last eight and a match against USA.
When the Czech went 3-0 up in the first period through Ales Hemsky, Roman Cervenka and David Krejci., with Cervenka added a fourth early in the second, it appeared that a rout was on the cards.
But the Slovak team bounced right back, scoring three without reply to set up a dramatic finale, with the Czechs only putting the result beyond doubt with minutes to go.
Baltic ice storm
In the other game, Latvia were surprise 3-1 victors over Switzerland, who had beaten them in their group stage opener.
An early goal from Oskars Bartulis and a double from Lauris Darzins helped Latvia on their way to a first ever Olympic quarter-final appearance, with their first men’s ice hockey victory since 2002.
Their reward is an encounter with defending champions Canada.