The 22-year-old, one of cycling's hottest prospects, beat Quintana by 39 seconds overall, allowing the Movistar rider to grab just a few seconds from him in the 110-km loop around Nice.
Another Team Sky rider, Michal Kwiatkowski, ended up third overall, one minute and three seconds off the pace and he also secured the green jersey for the points classification.
Sky have now claimed six of the last eight editions of the 'Race to the Sun'.
"I can’t believe that I just won Paris-Nice. It’s incredible for me. I’m really happy. I just can’t believe it yet," said Bernal.
“When some GC (general classification) riders started to attack I knew I could follow them, but also I know that I have a really good, strong team, and my team can control these races.
“So it wasn’t too difficult to be calm because I really believe in my team. They did a really, really good job. We knew it was the last day so they pulled really hard."
Bernal, who was impressive in helping Chris Froome and Geraint Thomas on the Tour de France last year, will make his debut as a leader on a grand tour at the Giro d'Italia this year.
(Reporting by Julien Pretot; Editing by Clare Lovell)
