Olympic combined bronze medallist Brignone was in pole after setting the fastest time in the morning's super-G, finishing 0.96 seconds ahead of the American star.
The Italian held her nerve superbly to lay down the second-fastest slalom run for a winning aggregate of one minute and 57.47 seconds.
"The only thing missing in my career was a gold medal, I’m so excited and happy about today," said Brignone.
"I was just focused on my skiing. For sure it was my perfect day."
Brignone admitted that Shiffrin had told her she had cranked up the pressure with her impressive super-G.
"My slalom is not the best but I can do good runs and we have a saying in Italian that 'until you're at the finish you're not finished'."
Switzerland's Wendy Holdener, a two-time former world combined champion, who claimed Olympic silver in Beijing, claimed second place, at 1.62 seconds, with Austrian Ricarda Haaser rounding out the podium (+2.26).
"The last couple of weeks for me it was hard to find the right balance, but arriving here I was feeling strong and skiing well. It's a perfect start for myself," said Holdener.
Holdener's teammate and two-time Olympic champion Michelle Gisin could only finish 3.43 seconds off Brignone's pace.
All eyes in the slalom had been primed for Shiffrin, and she did not disappoint as she tore up the first two-thirds of the Roc de Fer piste, gaining quickly on Brignone's aggregate time.
She seemed set to go top of the leaderboard but straddled the penultimate gate.
'No room for error'
"Of course I’m disappointed not to finish and not to get a medal, but I’m also quite excited because I was skiing really well," said Shiffrin.
"My mentality at the start of the slalom was to take all the risks, full-gas skiing from top to bottom and take the risk that it might not work, I might ski off the course because slalom is like that. There’s no room for error."
It means Shiffrin will have to wait until Wednesday's super-G in her bid to bag a record-equalling seventh post-WWII world individual gold. That would match Austrian Toni Sailer, Frenchwoman Marielle Goitschel and former Swedish racer Anja Paerson.
Shiffrin's dramatic exit left her mother Eileen holding her head in her hands in the finish area amid groans from the large crowd in the French resort.
The 27-year-old will hope there is no repeat of her disastrous outing at last year's Beijing Winter Olympics where she failed to finish the slalom, giant slalom and alpine combined - three events in which she had been a keen favourite.
She also failed to get close to the podium in either the super-G and downhill.
That stumbling form has not continued on the World Cup circuit this season, however, with Shiffrin winning 11 races (including five slaloms) to come within one of Ingemar Stenmark's overall World Cup record for victories (86).
One notable absentee from the start list was Slovakia's Petra Vlhova, who decided to sit out the combined to focus on next week's slalom and giant slalom.
The women's combined is the first of 13 medal events - comprising six women's races, six men's races and one mixed team event - at the biennial worlds in Meribel and Courchevel, which run until February 19th.
