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After race organisers tweaked the rules for the TTT to count times for teams based on the first rider across the line and individual times counting towards the general classification, Tour de France winner Vingegaard steered his team home and moved to fifth overall, three seconds behind new leader Cort (EF Education Easy-Post).
Cort and the EF team came agonisingly close to taking the stage and the yellow jersey, but had to settle for second as they were beaten by just one second by Jumbo-Visma, Australian team Jayco-AlUla finishing third, four seconds back.
While Vingegaard flourished again in the discipline, rival Tadej Pogacar and UAE Team Emirates had a day to forget, the Slovenian having to go full gas away from his teammates into the finish to bring them home 23 seconds behind Jumbo-Visma.
Pogacar now sits 10th in the general classification, 11 seconds behind Vingegaard and 14 behind Cort in top spot.
Vingegaard lauded the efforts of his teammates, including time trial champions Tobias Foss and Australian Rohan Dennis, in securing the victory as he looks well placed to snatch the yellow jersey as the race heads to the mountains after tomorrow's mostly flat stage.
"It feels great to have so many strong riders alongside me in this race," the Dane said.
"You can see that it can be really beneficial in stages like this. We tried to stick together with as many riders as possible for as long as we could.
"While we don't get to practice the team time trial as frequently as we would like, you can tell we have mastered this discipline. The time trial went very well, and at the end, we sprinted for every second.
"We naturally would have preferred to take a little more time, but we gave it our all to secure a solid position in the general classification. The coming mountain stages are going to be decisive. Tomorrow, the first uphill arrival is already a nice test."
Paris-Nice continues overnight with Stage 4, a mostly flat stage with a steep uphill finish on the La Loge Des Gardes. Watch the action from 12:55am (AEDT) LIVE on SBS and SBS On Demand.
