Both of Doak's rounds at the Castle Stuart Golf Links included an eagle, five birdies and a bogey to put him at 12-under 132 after 36 holes. He is seeking to be the first Scot since Colin Montgomerie in 1999 to win the Scottish Open.
But the leaderboard is crowded behind him with four players tied at 11-under and another five at 10-under.
Matthew Southgate had one of the rounds of the day with an 8-under 64 after six birdies and an eagle. J.B. Hansen and Ross Fisher each turned in 7-under 65s and Peter Uihlein shot 66 Friday. They are tied with Southgate for second.
First-round leader John Parry shot even-par 72 in the second round and dropped into a tie for 13th at 8-under. Also at 8-under is Phil Mickelson, who shot 2-under 70 Friday.
Doak had birdies at Nos. 2 and 3 and another at the sixth hole allowed him to make the turn at 3-under. He birdied the par-3 11th and then had an eagle at the 599-yard, par-5 12th. He dropped back a little with a bogey at 17 but closed with another birdie for sole possession of the lead.