In a tight competition where less than a second separated the top 12 after the first run, Feller edged McGrath by just 0.02 seconds.
Feller also takes the lead in the slalom rankings after a breathtaking second run in conditions made difficult by fog and the fact it was snowing.
Norwegian Alexander Steen Olsen topped the leaderboard after the first slalom run in fog, but the 22-year-old crashed out on the second run.
"You can never expect to win a race, especially after the first run," Feller said.
"I saw these young guns from Norway, they are going really hard, so I need to go a little bit more on the limit. That's what I did for the second run," he explained, adding that luck had been on his side.
Olympic champion Clement Noel, who was second in the last slalom at Madonna di Campiglio and lies fourth in the discipline standings, crashed out during his first run.
The 31-year-old Feller often gets on the podium in slalom and giant slalom but scored only his fourth World Cup success here, his second of the season after the slalom in Gurgl (Austria) in mid-November.
He is now 65 points clear at the top of the discipline standings, ahead of Marco Schwarz whose season ended when he injured a knee at the end of December and 125 points clear of Dave Ryding, the next active skier, who finished 21st on Sunday.
"That's an honour too but still a lot of races left," said Feller.
"I try to show some good skiing in the next races and looking forward for (the next slalom race in) Wengen."
The Swiss Marco Odermatt, winner on Saturday of the Adelboden giant but who is not competing in the slaloms, remains in control of the general classification.