McGrath led after the first run and kept his cool under intense pressure from former teammate Pinheiro Braathen to win by 0.47 seconds.
Pinheiro Braathen, fourth after the first run, put down an impressive second effort, but McGrath stayed smooth and avoided any major mistakes through the gates to take the win and move to the top of the World Cup slalom standings.
Norway's Henrik Kristoffersen was third for the 100th World Cup podium of his career.
France's Paco Rassat, who had been the leader in the slalom standings, failed to finish his second run.
"I can't believe it, I felt so nervous today," Vermont-born McGrath said at the finish.
"I took 100 risks today. I knew Lucas had taken the lead by a lot, and I know him too well. When he skis fast, you really have to go.
"That was one of the best second runs in my career."
The men's World Cup moves on to Kitzbuehel next weekend, where a slalom, super-G and downhill will take place.