Spanish teammate Dani Sordo was second and Ott Tanak third over the rough and rocky gravel roads to complete a podium lockout for the South Korean manufacturer in the Lamia-based event.
Hyundai lead Toyota by 35 points in the standings with three rounds remaining.
Neuville had a comfortable lead of more than a minute going into the final stage and the victory was the Belgian's second of the season and first since Monte Carlo in January.
Ogier's challenge disappeared completely when the Frenchman misjudged a corner and rolled 1.6km into the 18.2km final Power Stage.
The crew were unhurt and continued to the finish in the damaged car to secure the 13 points earned up to Saturday. Ogier had led the rally on Friday before suffering a turbocharger problem.
Neuville, who finished the 15-stage event one minute and 36.8 seconds clear of Sordo, now has 192 points to Tanak's 158 and Ogier's 154 with Toyota's Elfyn Evans on 140.
Tanak's podium was the 50th of the Estonian's world rally championship career.
The final day started after thunderstorms and heavy overnight rain, with muddy sections that later dried.
Neuville, chasing his first title after years in the top category, said he had been concerned about the roughness of the roads from the moment he checked out the stages on the limited-speed pre-rally recce.
"I knew that we needed a different approach than some of the other drivers to try to keep the advantage we have in the championship for the remaining rounds," said the Belgian.
"That objective and target has been the best, and paid off with victory and a good team result as well. We were not driving on the limit all weekend long to avoid any punctures and moments, and we kept all four wheels on the road.
"Now we have a good lead, the story will be to protect those points in the last three rounds."
The problems suffered by top-category drivers meant second-tier WRC2 contenders, led by Finland's Sami Pajari, made up the rest of the top 10.
The next round will be on gravel in Chile on the 26th- 29th September.