Meillard claimed victory by 0.26 seconds to become the first Swiss man to be crowned slalom world champion for 75 years.
Norway's Atle Lie McGrath was second with Germany's Linus Strasser in the bronze medal position.
France's Olympic champion Noel was leading after the opening run and looked on course for gold but he straddled a gate as he tried to dislodge Meillard from top spot.
Noel is yet to win a world championships medal having finished just off the podium two years ago.
World Cup slalom leader and defending world champion Henrik Kristoffersen of Norway finished a disappointing 13th.
"It's crazy, I know slalom can be tough and so many people can ski fast," said Meillard, who also won the team combined and was third in giant slalom.
"On the GS I tried to get the gold, so today it was a case of all in and see what happens."
Meillard's victory completed a dominant championships for the Swiss who claimed four of the five men's titles.
Switzerland finished top of the overall medals table with five golds and 13 medals. Hosts Austria were second with two golds in their total of seven medals.
The last Swiss man to win the slalom world title was Georges Schneider in 1950.