With Russian President Vladimir Putin watching in the crowd, the host nation's team took silver and France, despite first leg skier Jean-Marc Gaillard breaking a pole early on, claimed the bronze.
A day after Sweden claimed the women's 4x5km relay, the men's team took the early lead and never looked back, with Marcus Hellner holding his country's flag aloft as he crossed the finish line in one hour 28:42 minutes.
Norway were expected to dominate the cross-country events with World Cup leader Martin Johnsrud Sundby and double Vancouver champion Petter Northug in their ranks but disappointed again, finishing fourth.
The men have one gold and a bronze medal from the first four events.
Northug, who dropped out of the 15km classic because of poor form, produced the best effort for Norway with the third best time of the fourth leg, but it was too late.
On Saturday, Norwegian women blamed their miserable fifth place finish on their skis.
Eldar Roenning said Norway's men may have had the same problem.
"I think it's the same as yesterday. The skis were OK for the first two to three kilometres," he added.
"The waxers have been working all night to find the problem. This morning I was feeling OK but after three kilometres the skis felt very heavy. I pressed all the speed out of my skis."
Sweden, on the other had, had their skis to thank for success.
"The waxing is very tough and makes a very big difference on this snow," Hellner told a news conference. "We have succeeded here with our skis. That's a big reason of our success."
Sweden's Lars Nelson clocked the best time in the first leg and despite Daniel Richardsson and Johan Olsson slowing slightly in the second and third legs, they stayed in front and never looked in danger.
Nelson lost a ski at one point but managed to keep his position.
"I'm really happy with my lap. I lost my ski but I managed to recover. I just picked it up," he told reporters. "Luckily for me nobody took the chance to overtake so I don't think it had much of an effect.
"It was the lap of my dreams."
On a bright, crisp day at the Laura Cross country and Biathlon centre, Hellner, silver medallist in the skiathlon, had time to grab a Swedish flag just before entering the stadium.
Maxim Vylegzhanin produced a late attack to drop Frenchman Ivan Perrillat Boiteux and finish 27.3 seconds behind the Swedes, giving Russia their first cross country medal at the Sochi Games.
France snatched their first Olympic cross country medal since 2006, and just their second of all time, as they finished 4.6 seconds further back despite Gaillard's broken pole.
"I fell down on the curve and broke my pole," he told reporters. "If it was an individual race maybe my mind would give up but this is a relay.
"I changed the pole 20 metres after it broke and it wasn't good because they gave me a left one and I needed a right one, so they changed it again.
"We were starting to believe it would never happen," he added in a news conference, referring to France's two fourth-place finishes in Turin (2006) and Vancouver (2010).