Norway's overall World Cup leader Martin Johnsrud Sundby pipped Russian Maxim Vylegzhanin in a scramble on the line for bronze, prompting the Russian team to file a protest against the result, claiming that Sundby has cut across his opponent.
The protest was rejected but the International Ski Federation (FIS) said in a statement that Sundby had been given "a written reprimand for a corridor rules infraction".
"I was tired by the end of the race and I had fog in my glasses," the Norwegian told a news conference.
"Maybe I left my line a little bit but I don't think it changed anything. I'm sorry about that."
Russia, however, are likely to appeal the decision.
"The Russian Olympic Committee wants to appeal before the Court of Arbitration for Sport," Russian ski federation president Elena Vyalbe said in a statement on the Russian Olympic team website.
The appeal will not impact on Cologna, however.
"It's great, a dream come true," he said. "It's very special. I won here in the (2013) World Cup in Sochi, I just wanted to do the same again."
Cologna, the 15km freestyle Vancouver Olympics champion, sustained an ankle injury while jogging just before the season started and returned to the World Cup circuit last weekend.
"It's very special for me to win after my injury in November. I didn't expect to be on the podium," he said.
"I can't believe I won the first race."
Not being among the seeded skiers on Sunday meant Cologna started just behind the main pack of 20 but he quickly got among the leading bunch and never left it.
Heavily-fancied Norwegian Petter Northug, a four-times medallist in Vancouver, appeared at the front some five kilometres from home but eventually cracked and drifted in 17th.
Cologna made his break on the final short climb and never looked back, beating Hellner, who had won the event -- then called 'pursuit' -- in Vancouver by 0.4 seconds.
"It feels great," Hellner said. "I had a good feeling throughout the race. Dario was a little bit stronger. I couldn't follow him. I felt a bit stiff in the legs at the end."
In skiathlon, skiers race the first half of the course on classic technique skis, then exchange them for skating skis in the stadium and finish the event using the free technique. The timer does not stop while the skiers change skis.
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- Russian Olympic Committee