Hellner broke away from Emmanuel Jonnier of France and Martin Koukal of the Czech Republic on the final lap, quickly building a 15-second lead to decide the race with a couple of kilometers to go. Entering the ski stadium alone, he had plenty of time to grab a Swedish flag to wave as he paraded down the final straight, slowing his pace to a crawl to enjoy the moment.
"It was wonderful, getting to parade into the finish," Hellner said. "It's something we've all dreamed about doing. It's perfect; we couldn't ask for anything more."
The Swedish team of Daniel Richardsson, Johan Olsson, Anders Soedergren and Hellner finished the 4x10-kilometer race in 1 hour, 45 minutes, 5.4 seconds for its first relay gold since 1988.
Petter Northug used a furious final leg to secure silver for Norway, beating Jonnier and Koukal in a sprint to finish 15.9 seconds behind Hellner. The Czechs took the bronze, 16.5 seconds back as the French ended up fourth.
Norway was the favorite in the race because of Northug's unrivaled closing ability, but he started 37.5 seconds behind Hellner on the final leg, which proved too tall of an order even for him. Northug set a blistering pace from the start to pull within eyesight of the leading trio after two laps, but never came any closer to Hellner.
The Swede, who won the 30K pursuit, had saved enough energy to increase his pace as he entered the final lap, quickly pulling away from his French and Czech rivals and preventing Northug to ever get in position to use his sprinting ability at the end.
It was Olsson who paved the way for the Swedes after he pushed the pace on the second classical leg to shake off main rivals Norway and Germany. Only the Czechs and French — who had their best skiers on the second leg in Lukas Bauer and Vincent Vittoz — managed to keep up, as Germany's Axel Teichmann lost 27 seconds to Olsson and Norway's Odd-Bjoern Hjelmeset ended up 34 seconds back.
"It was my goal to push really hard," said Olsson, who took bronze in the pursuit. "I felt strong and could really turn it up on the second and third laps."
Soedergren and France's Maurice Manificat then took turns pushing the pace on the third leg to maintain their large lead, before Hellner did the rest for the Swedes.
"The guys did a perfect job," Hellner said. "I just had to close it out perfectly."
Northug said he knew he had no choice but to go full speed from the start.
"I knew if I did one of my best races we had a podium chance," said Northug, who won gold in the team sprint and bronze in the individual sprint. "On the second lap I knew that now it's time to push if you want the podium. We have to be happy with silver."