Second out of the start hut, the former world junior champion plunged down the fearsome Streif piste to take his first career downhill victory with a time of one minute 52.31 seconds.
Odermatt, who started the Hahnenkamm weekend with a narrow win in Friday's super-G, was the 12th man down the mountain and missed out by 0.07 as Franzoni celebrated with high-fives from his teammates.
Odermatt -- twice a runner-up in the Kitzbuehel downhill but still not a winner -- glanced at the timing screen and came to a halt, head down in disappointment and leaning heavily on his ski poles after his exertions.
France's Maxence Muzaton finished an astonishing third after putting everything on the line with bib 29 and long after the podium looked to be settled, with later starters setting some surprising times.
Italy's Florian Schieder was fourth and France's Nils Allegre fifth in a blue riband race watched by a cast of sporting luminaries including former Liverpool manager Juergen Klopp and Austria's 1976 Olympic champion Franz Klammer.
The victory was Franzoni's career second after winning this month's Wengen super-G and further burnished the 24-year-old's credentials as a gold medal candidate for his home Milano Cortina Olympics next month.
As a string of big guns failed to match his time, the tears of emotion began to flow.
Switzerland had won all four downhills before Saturday, Odermatt taking three and teammate Franjo Von Allmen triumphant in Val Gardena last month.
The two Swiss stayed one-two in the downhill standings, with Odermatt 165 points clear at the top after three wins and two second places. Von Allmen finished equal 16th after a big error and recovery in the closing stages.
Odermatt also increased his lead in the overall World Cup standings to 667 points over Norwegian-born Brazilian Lucas Pinheiro Braathen.