Bennett beat Australia's Caleb Ewan (Lotto Soudal) and Fabio Jakobsen (Deceuninck-QuickStep) on the 200km stage from Cepoy to Moulins/Yzeure.
“I didn’t train that much in the cold this winter and therefore had some troubles the last two days," Bennett said. "But I knew the form is there and today I felt a lot better.
"Of course, the stage was also easier, but there are a lot of great sprinters here in the peloton this year."
Winner of the first two stages, Dylan Groenewegen (Jumbo-Visma) was in the mix but did not feature in the end. He retained his hold on the overall lead ahead of Michał Kwiatkowski (Sky) and Luis Leon Sanchez (Astana).
"Groenewegen was almost unbeatable the last two days, but today everything went perfect for me," Bennett said. "The boys did a great job, they knew exactly what to do on the last kilometre and delivered me in a perfect position.
"It was a long sprint, but I knew I could do it. It seems like Paris-Nice likes me like I like the race."
The tough condition again took their toll with Fabio Aru (UAE-Team Emirates) the latest key name to abandon the race due to illness.
It was the first day without rain and heavy crosswinds after two demanding stages which featured both.
It took more than 40km before a break was allowed some leeway and it came from Delko Marseille Provence pair Ramunas Navardauskas and Alessandro Fedeli.
They were allowed a gap of up to four minutes were but doomed to fail with the catch coming with less than 40km to go.
Team Sky was active in capturing the intermediate bonuses with Kwiatkowski taking the maximum seconds on offer in both attempts. Handy in a general classification race which may be decided by just a handful of seconds.
"When there’s a chance to gain some time on GC by not expending too much energy, we are always up for it," he said. "There was plenty of chances to take bonus seconds in the sprints - there weren’t too many GC riders fighting for it.
"If you think about 14 seconds, it’s a huge amount. Think about trying to be 14 seconds faster in a time trial, for instance, that could mean winning the whole GC."