Austria's Johannes Lamparter took silver, while Eero Hirvonen clinched Finland's first medal of the Games with a bronze.
Oftebro started fourth in the ski race, 20 seconds behind Estonia's Kristjan Ilves, who came out of the ski jump with the highest score and a 15-second time advantage.
Ilves kept ahead of the other competitors for the first half of the race, but ultimately finished sixth.
"It was a really tough course and loose conditions, so it's really a tough race," said Oftebro, pointing to a near-crash on the third loop of the race. Warmer weather created slushy conditions on Wednesday, which sloshed snow around skis as racers climbed hills on the course.
"It was insanely tough out there. We spent almost half an hour on the course. I'd done a good job with the jumping, but it was incredibly heavy out there."
The win was Oftebro's third career Olympic medal and his second gold. In the 2022 Beijing Games, he won gold in the team large hill event and silver in the individual large hill competition.
The 25-year-old's gold medal marks the seventh for Norway at these Games and their fourth at Milano Cortina in an event featuring cross-country skiing.
Compatriot Johannes Klaebo has won two golds here in cross-country skiing, and the country also took victory in biathlon.
Wednesday's competition combines ski jumping and 10km of Nordic skiing. Those who perform better on the jumps get a time advantage in the cross-country ski portion of the event.
"The jumping hill was really close this morning. We were all close together with very tight gaps. It was a very hard race - like a selection - but the best won at the end," said Austria's Lamparter, who clawed back from starting sixth after the ski jump to claim the silver.