Venier's second career World Cup victory came thanks to a winning time of 1min 33.06sec, 0.39sec ahead of Switzerland's Lara Gut-Behrami, with Canadian Valerie Grenier rounding out the podium (+0.71).
All eyes had earlier turned, however, to Shiffrin, the leader of the women's overall World Cup standings losing balance off a jump before one of the toughest turns on the testing Olympia delle Tofane course and sliding into the side netting.
She remained prone until the arrival of the medical team, after which she got to her feet, unable to put weight on her left leg, leaving the piste with the aid of her poles.
The race was interrupted for more than 20 minutes as Shiffrin was eventually evacuated by helicopter.
It was just Shiffrin's second downhill race of the season.
The five-time overall World Cup winner has a record 95 victories to her name.
She has already won seven World Cup events this season, including her previous downhill in St Moritz in December.
Shiffrin's boyfriend, Norwegian Aleksander Aamodt Kilde, will miss the remainder of the season after his own heavy crash in Wengen earlier this month that left him with a dislocated shoulder and cuts to his face and calf.
The men's circuit has also been hit by season-ending injuries to Austrian Marco Schwarz and France's Alexis Pinturault.
Shiffrin remains 340 points ahead of Gut-Behrami in the women's overall standings.
Among other racers who failed to finish the Cortina course that will be used for the women's speed events at the 2026 Winter Olympics was Switzerland's reigning Olympic downhill champion Corinne Suter, who was also evacuated by helicopter.
Her teammate, Olympic combined gold medallist Michelle Gisin, and Italy's Federica Brignone, fourth in the standings, also crashed out.
Racing in Cortina continues with a second downhill on Saturday and a super-G on Sunday.
