Their quartet of Marcus Hellner, Lars Nelson, Johan Olsson and Daniel Richardson led from start to finish and completed the course in one hour 28 minutes 42 seconds.
The battle for silver and bronze was won by Russia - who were watched by President Vladimir Putin.
The bronze was taken by France - their first medal in the event.
A day after their women's team came from behind to earn a narrow relay victory, Sweden's anchor Hellner skied alone for the entire fourth leg and grabbed a Swedish flag to wave as he entered the stadium and proceeded unchallenged down the final straight.
Hellner started the final leg with a 14-second lead over Russia's Maxim Vylegzhanin and quickly extended the gap, eventually winning by 27.3 seconds.
It was another disappointing day for Norway, who had fallen a minute behind by the second exchange and ended up fourth, a day after their heavily favoured women also failed to get a medal.

The internet retailing giant also said it expected to report a bigger-than-expected loss in the next three-month period.
Amazon shares plunged over 10% in after-hours trading in New York.
Investors have long been wondering when Amazon will turn its significant revenues into profits for shareholders.
Amazon has been spending heavily in various new initiatives, including its Amazon Fresh grocery delivery service in the US, and its $1bn acquisition of video game streaming site Twitch.
That has hurt profits at the firm, with operating expenses growing to $21.1bn, compared with the $17.1bn last year.
Investors have been tolerant of Amazon's policy of reinvesting profits back into the firm. But patience has been wearing thin in recent months.
Shares in the firm have fallen nearly 20% since the beginning of this year.
In a statement accompanying its earnings, Amazon founder and chief executive Jeff Bezos chose instead to focus on the firm's holiday offerings during the crucial period in the run-up to Christmas.
"As we get ready for this upcoming holiday season, we are focused on making the customer experience easier and more stress-free than ever," he said.

The rally is being held to mark the 25th anniversary of the creation of the Islamist militant movement, Hamas.
There were also reports of clashes between protesters with Israeli soldiers elsewhere in the West Bank.
On Thursday, a Palestinian teenager was shot dead by an Israeli border guard at a checkpoint in Hebron.
Israeli police said he had attacked a guard and threatened him with what turned out to be a metal toy pistol.
Tensions have been running high in Hebron in the past week following repeated clashes between soldiers and stone-throwing youths.
Hebron is home to about 180,000 Palestinians and some 500 Jewish settlers who live in the centre of the city, guarded by Israeli troops.
On Thursday, the Palestinian Authority allowed Hamas to organise a rally in the West Bank for the first time since 2007. Some 5,000 people took to the streets of Nablus to celebrate the group's anniversary.
Hamas and the rival Fatah faction, which dominates the PA, have made conciliatory gestures towards each other since the end of last month's Israeli offensive on Gaza, which Israel said it launched to stop rocket-fire.
"Hamas steadfastness and victory in Gaza was a big victory for all Palestinian people," Amin Makboul, a Fatah leader, said in a speech at Thursday's rally in Nablus.
A rift developed between the two groups after Hamas won legislative elections in 2006 and came to power in Gaza a year later. Repeated attempts at reconciliation have so far failed.
Defending champions Sweden took gold in the men's cross country 4x10km relay at the Winter Olympics in Sochi.
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Amazon has reported a third-quarter loss of $437m (£273m) - up significantly from the $41m loss it reported for the same period last year.
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About 3,000 Palestinians are marching towards an Israeli checkpoint in Hebron, not far from Jewish settlements in the centre of the West Bank city.