Cologna, who earlier this week was still walking around with a splint on his injured right ankle, attacked with less than a kilometre left in the 30km race to finish ahead of Swede Marcus Hellner in second.
Overall World Cup leader Martin Johnsrud Sundby of Norway outsprinted Russian Maxim Vylegzhanin in the closing stages to deny the host nation bronze.
A short statement issued by the technical delegate said a "jury decision" affecting the result was in progress, though all of the top three were presented at the medal winners news conference.
Sundby appeared to slightly change his line during the sprint but he did not think it should affect the final results, which were published over an hour after the end of the race.
"I was tired by the end of the race and I had fog in my glasses," he 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."
Norway's Petter Northug, a four-times medallist at the Vancouver Games four years ago, cracked in the final run-in to finish a distant 17th.
"It's great - a dream come true," said Cologna. "It's very special. I won already 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 just last weekend.
"It's very special for me to win after my injury in November. I didn't expect to be on the podium some months ago.
"I can't believe I won the first race."
Not 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 Northug finally appeared at the front some five kilometres from home but eventually cracked as Cologna, Hellner, Sundby and Vylegzhanin powered away with 2km left.
Cologna made his break in 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."
Sundby had mixed feelings.
"I started here to get a gold but I'm third," he said. "For sure a medal is good but I went for gold and bronze is a disappointment."
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.
(Additional reporting by Dmitry Rogovitskiy; Editing by Peter Rutherford)
