The 26-year-old Liverpudlian carded a second successive 66 to put him on an eight under par total of 132, a score matched by Hanson.
His late surge began on the 15th when despite missing the fairway he managed to pitch to 15 feet and sink the putt.
Dougherty then got up and down from sand at the 17th, another par five, and hit a peach of a four-iron to 10 feet on the next.
Dougherty and Hanson are two clear of Denmark’s Soren Kjeldsen and Swede Patrik Sjoland, with former Ryder Cup pair Paul Broadhurst and Peter Baker, Scot Gary Orr and another Swede, US Tour-based Daniel Chopra, one further back.
Dougherty has fallen to 15th in the Ryder Cup points race following the death of his mother after a heart attack in April.
“The Ryder Cup would be lovely and I would be an idiot if I said it does not matter, but more important is enjoying my golf again,” he said.
“I’ve had my reasons to feel a bit down, but considering how I’ve played the last few months I’ve a lot to smile about this week.”
The SAS Masters is the largest annual sports event in Scandinavia and a European tour event. The tournament has been played since 1991 and this year is being held at Arlandastad Golf, 30 kilometres north of Stockholm.