Odermatt was a full second faster than Austrian silver medallist Raphael Haaser, with Norway's Adrian Smiseth Sejersted taking the bronze on another bright and clear morning in the Austrian resort.
"It was really a perfect run, I couldn't do it any better," said Odermatt. "I had the best feeling from the third gate, I felt my skis worked perfectly, I did exactly what I wanted."
The three-time overall World Cup champion, who won gold in downhill and giant slalom at the 2023 world championships in Courchevel, arrived in Saalbach as leader of the World Cup super-G, downhill, giant slalom and overall standings.
The gold was Odermatt's first medal in super-G at a major event.
"It means a lot," he told Eurosport television. "It's unbelievable to be a world champion in three different disciplines... I'm just happy to be here, healthy and in good shape."
Austrian Vincent Kriechmayr, his closest rival, finished fourth, missing out on a medal by 0.05.
"My run was not good enough," said the Austrian. "It's good for our team to have Raphael Haaser in second place but incredible what Odermatt shows today."
Canada's defending world super-G champion James Crawford was way off the pace, 3.41 seconds slower than Odermatt and out of the top 20.
Odermatt's gold was Switzerland's first of the 13-day championships.
The women's downhill is the next race, on Saturday, with Czech Ester Ledecka fastest in final training.
Italy's 2018 Olympic champion Sofia Goggia, whose career has been marred by a series of injuries, fell after a jump and failed to set a time but told RAI television she was unhurt.
"I probably caught a little bit of an edge and made the movement wrong, but everything is OK. I risked it a bit but I was lucky," she said.
American great Lindsey Vonn, who failed to finish Thursday's super-G after hitting a gate, returned to the slopes but was only 21st.
Vonn, 40, won the downhill at the 2009 Val d'Isere championships and 2010 Vancouver Olympics but has been feeling unwell in Saalbach.
"Hoping my energy levels get better so I can have a chance to ski my best," she said on Instagram.