The 24-year-old Slovenian produced a thrilling solo surge on the 117.2-kilometre eighth stage, chiefly contested in the hills surrounding Nice.
His race-winning move came on the final climb, the Col d'Eze, as the UAE Team Emirates man left his rivals to scrap it out for second place before tearing away to the finish line on the Promenade des Anglais.
Pogacar took the stage by 33 seconds. Jonas Vingegaard (Team Jumbo-Visma) was second to cross the line on the sea front, with Pogacar taking the overall tour victory by 53 seconds from France's David Gaudu (Groupama–FDJ).
Vingegaard, the reigning Tour de France champion, picked up third place on this occasion in the general classification standings.
Pogacar won the one-day Clasica Jaen Paraiso Interior in Spain early last month, and then went on to dominate the five-day Vuelta a Andalucia.
The latest success is a further step towards the grand tours that await later in the year, with Pogacar electing to race at this event, on the roads where he does much of his training, rather than head to the Tirreno-Adriatico in Italy. That race, running concurrently, was won on Sunday by Primoz Roglic after Pogacar's victories there in 2021 and 2022.
"It was always my goal, my dream, to win Paris-Nice as well and now that I did it, it's incredible," Pogacar said on Eurosport.
"They say attack is the best defence and I really know these roads. A lot of training is done here, so I knew exactly how my legs were and on the final climb how much I could spend to come to the top and I calculated great."
Pogacar will turn his attention to next Saturday's Milan-San Remo one-day classic, satisfied to have got the better of a strong field.
"The competition here was really, really huge and to be alongside David Gaudu and Jonas Vingegaard on the podium is special because they are really top-class riders," Pogacar said. "If I don't win anything until the end of the season it's still not bad, so I can be more relaxed."
Arkea-Samsic rider Quintana launched a late attack in the closing four kilometres, crossing the line 47 seconds ahead of Tiesj Benoot.
It means Quintana – who crashed in stage two – finished sixth in the general classification, with Max Schachmann having maintained his overnight lead to claim the overall triumph.
With Sunday's stage cancelled due to the spread of coronavirus, French rider Romain Bardet criticised race organisers, claiming he could not understand why Saturday's event was going ahead.
After the race's completion, Quintana also referenced his concerns over the ongoing pandemic, acknowledging his main focus was now on being with his family.
"Now we'll try to return to Colombia, spend time with the family while this important problem for the world is resolved," the 30-year-old told reporters.
"We are aware of what is happening, we've finally finished and we will also be quarantined so that this virus does not continue to spread.
"We have to listen to the authorities so that this does not get out of hand and we can all return to work soon."
Despite a difficult start to the event, Quintana was thrilled to have finished on a high with a third stage win of the season.
"I always try to win like this, with elegance and a good attitude," he added. "We were highly motivated to do things well and have been working hard.
"The team worked hard to catch the break and then I did what I had to do. There was nothing I could do for the GC, so I knew I had to attack today, because I wanted to bring joy to the team, because of the effort that everyone has made. It is a gift for all of them. I always demand a lot, but here are the results."
While the stage belonged to Quintana, it was Schachmann who claimed the general classification victory.
Team Sunweb's Benoot started the day 36 seconds behind Schachmann, who also had to deal with challenges from Vincenzo Nibali, Thibaut Pinot and Sergio Higuita.
With Quintana already far up ahead, Benoot rolled the dice with just over 1,000m to go, and although he established a gap, Schachmann piggie-backed onto Higuita's chase to ensure an 18-second winning margin.
"It was a really hard finish, in the last three kilometres I worked through hell and a world of pain," Schachmann said.
"But now it's like being in heaven. Every little bit of pain in my legs was worth it. This is one of the biggest wins of my career and one of the most important steps."
