The 2019 world champion finished the sixth stage of the gruelling Acropolis Rally 21.8 seconds clear of Spaniard Dani Sordo with championship leader Thierry Neuville a further 23.4 behind.
Toyota's Sebastien Ogier, the eight-times world champion who started the season on a part-time schedule but is now his team's top hope, was fourth and nearly two-and-a-half minutes off Tanak's pace.
"We need to be very grateful for a trouble-free day," said Tanak, whose team are leading the manufacturers' standings.
"It has been very difficult with the temperature and roughness."
Ogier won three of the day's rocky gravel stages and led by 5.9 seconds after the morning loop but was slowed by a turbo boost pressure problem on stage five while Tanak surged ahead.
"There was not much we could do, turbo is broken," said the Frenchman.
"That's motorsport sometimes. It's not the day we were hoping for."
Neuville, who opened the road in the morning as overall leader, was fastest in the day's final stage after a difficult start with engine problems.
"We have seen a lot of problems for everyone so it could have gone much worse for us," said the Belgian.
"With the position we are in, we are good."
Toyota's Elfyn Evans, another title contender, had to stop on stage one to change a wheel and then lost nearly nine minutes with turbo issues and ended the day 17th.
Toyota's Takamoto Katsuta won stage two but retired for the day with a broken rear suspension after he misheard a pace note. M-Sport Ford's Adrien Fourmaux was also sidelined after he hit a rock and broke the steering.
Neuville led Ogier by 27 points going into the weekend, the Belgian on 168 to the Frenchman's 141 with Tanak on 137 and three rounds to come after Greece.
There are six more stages on Saturday.
