It was Miller's first major title and enhanced his reputation as one of the best all-around skiers in the world.
Norwegian veterans Lasse Kjus and Kjetil Andre Aamodt won the silver and bronze medals as the top three were separated by a mere .18 of a second.
Miller was in 17th place after the downhill portion of the competition, almost three full seconds behind Kjus. He climbed to fourth after the first slalom run and then produced another outstanding effort to nip Kjus for the gold.
Miller turned in a combined time of 3:18.410 while Kjus finished in 3:18.480. Aamodt earned the bronze with a 3:18.540. Pierrick Bourgeat of France was fourth, Silvan Zurbriggen of Switzerland finished fifth and Markus Larson of Sweden wound up sixth.
The best finish for the powerful Austrian team came from Rainer Schonfelder, who was ninth. Austrian Benjamin Raich was second going into the second slalom run, but he missed a gate and did not finish.
Through three of the 10 events that are staged at the World Championships, the United States has more medals than the Austrians. Miller's gold gave the Americans four medals overall while Austria has three.
"Being on top in such a tight competition is a great success," said Miller, 25, who also overcame a big deficit to win the combined silver medal at last year's Winter Olympics.
"There was quite a big gap after the downhill so I just decided to go for it and that's what I did. Once your momentum starts building like that, we want to race our hardest here. When you've got a team feeling like that, it's contagious."
Aamodt, who won the Olympic combined ahead of Miller at Salt Lake City, captured his 11th World Championship medal. He also has seven Olympic medals.
"A medal is a medal -- I'm very happy," said Aamodt, 31. "I felt a bit tired after the downhill. The slalom course was not very demanding. Maybe I should have taken more risks."
Miller stands second this season behind Austrian Stephan Eberharter in the race for the World Cup's overall title. Eberharter, however, excels chiefly in the speed events while Miller has grown into an outstanding skier in all five disciplines.
Although Miller is best known for his technical expertise, he managed a silver medal behind Eberharter last week in the super-G.
The other American medals during the championships came from Kirsten Clark (silver) and Jonna Mendes (bronze) in the women's super-G.
The next competition will be the men's downhill on Saturday, where Eberharter will be the favorite.
Swim Week Miami Beach 2014 [PHOTOS]