Tanak won the fifth round of the championship by 37.7 seconds, with Neuville second and his Hyundai team mate Dani Sordo third.
Ogier, who had won three of the four rallies before Argentina, finished fourth for M-Sport Ford. He now has 100 points to Neuville's 90.
"I can't say it was easy. I was pushing really hard and living on the edge on Friday and Saturday," said Tanak, who had damaged his car's steering in the opening special stage on Friday.
He went on to win 10 stages of the event based in Villa Carlos Paz, near Cordoba and some 700km to the north-west of Buenos Aires.
Neuville added five points to his tally by winning the final Power Stage, with Ogier second.
"It wasn't an easy rally for us and we need to work on some areas to improve. But when you come away from a difficult event with 16 points, it's not bad," Ogier said.
The next rally is in Portugal from May 17-20.
(Reporting by Alan Baldwin in Baku, editing by Ed Osmond)
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