Cologna, who also won last Sunday's skiathlon, dominated a race again held in very warm conditions at the Laura Biathlon and Cross-Country Complex. Sundby finished 13th.
"It's amazing. I couldn't believe the first gold medal after being injured -- and now the second. It was the perfect race," Cologna told reporters.
"I knew it would be hard and I was prepared for it. The first gold was emotional after coming back from injury, the second is unbelievable."
Temperatures reached 14 degrees Celsius and many skiers again wore short sleeves, with at least one of them wearing shorts on snow that resembled cottage cheese on some parts of the course.
To add to Norwegian woes, arch-rivals Sweden had two men on the podium, Johan Olsson and Daniel Richardsson taking silver and bronze.
"It means everything," said Richardsson.
"It will mean a lot to my family. It means a lot to Sweden. I think a gold medal will come."
Sundby would like to think so, too, but he sounded quite pessimistic.
"I'm very disappointed, but I can't explain such a bad result of the Norwegian team," overall World Cup leader Sundby told reporters.
"We are in bad form, but it's not due to the track or the weather. Now we have to practise hard to do our best in the relay on Sunday."
Norway, who have three men in the top four of the World Cup standings, have won bronze in the skiathlon and their only title came from Ola Vigen Hattestad in the sprint. Northug, whose early season was hampered by a virus, has been completely out of form.
He did not even take part in the 15km classic which was dominated by Cologna, who has fully recovered from an ankle injury he sustained last November.
Cologna made a cautious start but was in first place at the 8km mark and he never lost the lead, becoming the first skier to win an Olympic 15km race twice in a row.
A gracious Cologna waited at the finish to greet Peru's Roberto Carcelen, who crossed the line almost 28 minutes off the pace waving his country's flag as he was roared on by the crowd.
Norwegian men now have the relay, the team sprint and the mass start to make up for a disappointing Games in cross country.
At the 2010 Olympics, they won two gold medals, one silver and one bronze.