Organizers had to cancel Tuesday's training because of heavy snow and opted for a late start to Wednesday's session in order to best prepare the famed Lauberhorn piste.
Heel timed two minutes, 39:04 seconds down the strength-sapping 4,422-metre-long course, the longest on the World Cup circuit, 0.30 seconds ahead of Fill, with Swiss racer Patrick Küng in third 0.45 seconds behind.
"I didn't think I was this fast but knowing I can be definitely gives me confidence for the races," said Heel.
"We will see how the slope develops, some sections were still a bit soft due to the heavy snowfall from yesterday but they have done a great job and some sections are already icy," he said.
"I am confident that by Saturday the course will be in great shape."
After a second training session on Thursday, the men compete in the super-combined on Friday, kicking off with the slalom followed by an afternoon downhill in expectation of more snow in the morning.
Saturday sees the downhill proper with the slalom competition scheduled for Sunday.
In women's skiing, races cancelled in Garmisch-Partenkirchen, Germany because of a lack of snow have been re-scheduled for January 25th-26th in the Italian resort of Cortina d'Ampezzo, organizers said.
It means Cortina will hold two successive weekends of racing, the women already in situ for a downhill and a super-G this Saturday and Sunday.
That programme will be mimicked the following weekend to make up for the Garmisch races, with downhill training to be held on January 23rd-24th, the International Ski Federation said.