Erlandsson had 10 birdies for a 62 and second place. Hedblom won his third European Tour title at 13-under 275.
This was my first on European soil, so to do it at the Home of Golf ' Scotland ' is unbelievable, Hedblom said.
Former British Open champion Paul Lawrie closed with a 69 to share third place with defending champion Gregory Havret (67), three strokes behind the leader.
Gary Orr also made 10 birdies for a 64 on Gleneagles Course, but had a double bogey on No. 5 and finished fifth.
Erlandsson birdied the second and fourth holes, then seven in a row from the sixth, just one shy of the European Tour record. He also birdied the 17th.
I was trying to not let things run away in my head too much, he said. I played free and that was the key.
The longest putt in his birdie run was from 20 feet at the 10th.