McDowell, who turned 23 on Tuesday, broke the Kungsangen course record by one shot in his first competitive round over the layout.
This is the third appearance as a pro on the European Tour for McDowell, a former Walker Cup team member who has been labeled as a future star. He missed the cut at the Great North Open, but tied for 27th the next week at the Irish Open.
"I did not feel that good for the first five or six holes but scrambled and hung in there and things got better from then on," said McDowell, who won nine college tournaments while at the University of Alabama. "This is a dream start."
Adam Scott was alone in second after a 65 while Warren Bennett, Matthew Cort and Grant Hamerton all shot a 66 to tie for third.