Kris Meeke and Jari-Matti Latvala finished second and third respectively to ensure a first clean sweep of the podium for the Japanese team since 1993 and the first in the world championship since this rally started four years ago.
Tanak took control of the four-day contest on Saturday after title rival Neuville's challenge came to a premature end when he blew a tyre on his Hyundai i20.
Brake problems meant Tanak had to settle for eighth spot in Sunday's final power stage but he was pleased to have made huge strides towards a maiden world championship title with four races to go.
"We started to have some issues in the previous stage so I couldn't push. We only had one brake at the front," he said.
"I'm not really happy about that but we're here and I am happy about that. The team has missed out on a 1-2-3 a few times so it is good to do that finally."
Citroen's team strategy allowed reigning world champion Sebastien Ogier to climb from eighth to seventh but he still trails Tanak by 40 points and Neuville by seven.
The championship next moves to Rally Turkey, which takes place in Marmaris from Sept. 12-15.