Von Allmen claims second world gold as Swiss sweep team combined
Von Allmen, who won individual downhill gold on Sunday, had been second fastest down the downhill section while Meillard was 10th quickest in the slalom, good enough for a winning aggregate time of 2min 42.38sec.
Alexis Monney, fastest in the downhill, and Tanguy Nef won silver, at 0.27sec, while the ski-mad country's fourth-ranked pairing of Stefan Rogentin and Marc Rochat claimed bronze, a further 0.16sec adrift.
"It's crazy," said Von Allmen, whose two gold medals emulated American Breezy Johnson, who backed up her downhill win with victory in the women's combined alongside Mikaela Shiffrin.
"But we shouldn't have too many races like this because it was crazy to follow, nerve-wise."
Meillard added: "Having three Swiss teams on the podium, it's incredible.
"I don't know what's happening in this team, everyone is crazy."
The pair's victory means that Switzerland have won the opening three of the five men's races in Saalbach, team leader Marco Odermatt having stormed to super-G victory.
The sole medal for the Swiss women has been a team combined silver for the experienced duo of Lara Gut-Behrami and Wendy Holdener.
The latter was also part of the foursome that claimed silver in the mixed team parallel, the opening event of the champs that run until Sunday.
Tricky conditions
Wednesday's race had been delicately poised after the opening downhill, the slalom made all that harder as conditions deteriorated in warm temperatures following early rain.
Benjamin Ritchie held his nerve to take the lead for the United States along with Ryan Cochran-Siegle with 11 racers to come.
There was then a dramatic flurry of racers who failed to finish after straddling gates high up the course as they pushed for victory.
Among them were Switzerland's Daniel Yule, France's Olympic champion Clement Noel and Austrian fan favourite Manuel Feller.
Rochat did enough to ensure his Swiss pairing snatched the provisional lead.
Then it was down to the last three in tough, rutted conditions.
But there was immediate heartbreak for Dominik Paris and Alex Vinatzer as the latter skied out.
Then came the 28-year-old Meillard, with a 1.06sec advantage over Rogentin and Rochat. And he made no mistake in his 13th world championship start.
He perfectly judged his attack, not overforcing his speed down the tight, turny course on the Ulli Maier piste.
That left Monney's partner Nef, with a paltry lead of just two-hundredths of a second from the downhill section -- and everything to do.
He immediately lost time up high, but pushed once more into the lead.
The 15,000-strong crowd packed around the finish area waited with bated breath as he laboured down, cheering as he battled over the line in second place, pushing Ritchie and Cochran-Siegle into fourth (+0.69sec).
Incredible feeling
Nef was quickly enveloped by Von Allmen and the four other Swiss podium-topping racers who roared in delight at their dominant display in the Austrian resort.
"The feeling is incredible," said Nef. "I didn't know there were three Swiss teams on the podium.
"Alexis had an incredible race this morning, so there was a bit less pressure. I didn't have to take as many risks. It's my first podium and it's with two other Swiss teams!"
Monney, who also claimed bronze in the individual downhill, added: "It wasn't easy to watch! There was pressure here in the finish area, but I was relieved to see Tanguy cross the line with second place. It's great to have three teams on the podium."
Three of the four Austrian teams entered bombed out, leaving Daniel Hemetsberger and Fabio Gstrein as the sole finishers, in fifth at 0.80sec.
"It was a long slalom. Conditions were not that good, but it makes the event very interesting," Gstrein said of the newly formatted combined that will also feature at next year's Winter Olympics in Milan/Cortina d'Ampezzo.
Hemetsberger was magnanimous in defeat.
"We have to be fair, they were better than us today," he said. "The two Swiss young guns were quite good in the downhill so they had a good result for the slalom skiers."