The Glaswegian continues to make a mockery of his maiden showing on the Oceanico Victoria course adding a second-round 64 to his opening 67 and moving to a share of fourth place on 11-under par.
South African Hennie Otto (63) and the England pair of David Lynn (65) and Paul Waring (64) share the lead on 12-under par.
Doak capped his round holing a 10-foot putt for eagle at the par five 12th hole just minutes after landing a 140-yard 9-iron to six feet for birdie at the 11th.
The Scot began his round with back-to-back birdies when landing a 142-yard 8-iron to three feet at the first and hitting a wedge from 102-yards out to six feet at the second.
And just when Doak looked likely to drop a shot at the last after his approach shot was way right, he chipped to four feet and knocked in the par putt.
"It was a fantastic round of golf and after getting off to such a great start, it was just really steady after that and to end with a bogey-free is really nice and something that I have not been doing," he said.
"So all I need to do is just walk up and hit the shots and also it was a bit windy today and while it's much hotter down here than back home, growing up in the wind in Scotland is something I've long been used to."
Doak had posted a career low round of 63 in his last event, the Alfred Dunhill Links Championship while his Portugal opening 36-hole effort is also a career best for the 35-year-old whose best finish in some 78 Tour events is sixth in last year's Lyoness Open in Austria.
"These two rounds are easily the best I've played on Tour even though I have been up there contending before," said Doak. "Everything is just coming so natural to me. I'm hitting the fairways and the putts are dropping.
"And the big difference is these have been two very relaxed rounds rather than two tension filled rounds. Even when I miss a green my short game is good enough to get up and down, and the putter is good enough to hole the putts so what's there to worry about?
"I'd love to give myself the luxury of thinking now about going home with a new trophy, but there is a long way to go just yet."
He arrived on the Algarve lying 112th on Race to Dubai and two spots outside of retaining automatic Tour membership with the Portuguese event and next week's Perth International in Australia remaining.
Victory would send Doak well inside the top-60 and also into the end-of-season Final Series starting next fortnight in Shanghai.
Paul Lawrie continues to struggle with the same mystery energy-sapping bug he had last week in France for the Seve Trophy. The former Open Champion put that aside to post five birdies in a bogey-free 66 to move to seven under par.
"I played some lovely stuff today but must have missed six putts inside 10 feet and just can't seem to get the ball in the hole," he said. "So in saying that, I should be nine, 10 or 11 under and not seven, so it's disappointing to say the least."
n Rory McIlroy's battle with former management company, Horizon Sports heads to the courts next week. A preliminary hearing is listed for 9am on Monday at the Commercial Division of the High Court in Dublin.