Ogier was fastest on all three of Saturday afternoon's stages, thriving as the worst of the loose gravel that had hampered him in the morning had been cleared during the first pass.
He went into Saturday only sixth, 25.9s off Latvala, and couldn't close that gap much in the morning.
But his afternoon charge brought Ogier firmly into contention, as he demoted Kris Meeke and Andreas Mikkelsen to third and fourth.
Jari-Matti Latvala beats Sebastien Ogier to claim win in Portugal
Latvala rued his tyre management on the long final stage in particular, where he initially looked set to inch slightly further away from Ogier before ending up 5s down on his team-mate.
Ogier will start Sunday's concluding three-stage loop 9.5s behind Latvala, and having saved an additional soft tyre.
Having closed on Latvala during the morning, Citroen driver Meeke struggled to match the VWs around him in the afternoon.
He lost second to Ogier on the last stage and fell 10s adrift, hanging on to third by just a second over Mikkelsen - who spun over the Fridao stage's finish line.
Ott Tanak has cemented his fifth place in M-Sport's new Ford Fiesta, while Hyundai team-mates Dani Sordo and Hayden Paddon have been swapping sixth position.
Mads Ostberg is just behind that battle, having struggled through the afternoon with a lack of boost on his Citroen's engine.
Follow the deciding stages of the Rally of Portugal as they happen with AUTOSPORT Race Centre Live from 8am UK time on Sunday
LEADING POSITIONS AFTER SS13:
Jari-Matti Latvala builds Rally Portugal lead
Rally Portugal stage cut due to fires