The Northern Irishman leads Australian Adam Scott, who shot 65. Three-time champion Colin Montgomerie opened his title defense in 1-under 70 at the Kungsangen Golf Club.
McDowell, who turned 23 Tuesday, was a late entry into the event, and didn't even get to play the back nine in practice.
'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.
The former amateur standout won six individual tournaments during his junior season at the University of Alabama-Birmingham. He won a total of eight tournaments in his three-year collegiate career.
In addition to his All-America selection this year, he was Conference USA Player of the Year for the second straight year and GolfWorlds College Player of the Year.
'I knew that most of the top golfers in the world play college golf in America so I knew if I could get into the top 15 I would be ready to turn professional. Being top ranked this year has reinforced my belief,' he said.
This is McDowells third professional event on the European Tour. He missed the cut in his debut at The Great North Open, and then tied for 27th at the Murphys Irish Open, shooting 65 in the third round.
He has seven exemptions in which to earn enough money to make his card for next year.
Thursday, following an hour-long weather delay, he recorded seven birdies and no bogeys in establishing a new career low. After starting on the back nine, he birdied four of his final five holes on the front side.
'I'm very happy to be here, and to break the course record is a dream start,' McDowell said.
'The top priority now is to get a card for next year and a good result here would not be a big surprise because I have been playing well since turning professional before The Great North Open at De Vere Slaley Hall, but I was not scoring well.'
Scott, who won this years Qatar Masters, bogeyed the par-3 12th, his third hole of the day, but made five birdies to go along with an eagle-3 at the par-5 fifth.
Scott played alongside Montgomerie in the first round. Scott employees caddie Alastair McLean, who was let go by Montgomerie in May after 10 years of service.
Englishmen Warren Bennett, Matthew Cort and Grant Hamerton are two back after a trio of 66s.
Ryder Cuppers Niclas Fasth and Jesper Parnevik are tied for low Swede. Parnevik, a two-time winner of this event, matched Fasth's 67 in round one.
American Jeff Sluman, who was in the country for good friend Per-Ulrik Johansson's wedding, decided to stick around for the tournament. He shot 2-under 69.
Full-field scores from the Volvo Scandinavian Masters