"A 67 around here is a good score," Scott said. "It was a bit of a slow finish but it was a good way to open up.
"I felt like I left a couple out there, but my game was in pretty good shape other than that and four rounds like that might go a long way this week."
Left-hander Cullen eagled the par-4 11th, holing out from 65 yards with a 60 degree wedge. He followed with birdies at the 12th, 13th and 17th to open a three-stroke lead at 7-under but came back to the field with a bogey on 18.
"Any time you shoot 6-under around a course like this you have to be happy," Cullen said.
Zimbabwe's Brendon De Jonge and Australia's Peter O'Malley had 68s and were in a group of eight players at 3 under.
Jarrod Lyle, returning to play after his second bout with leukemia, opened with a 72 and was level with Vijay Singh at 1 over.
After an emotional start, Lyle settled into a round and mixed three birdies and four bogeys.
"It was a feeling I thought I would never experience again," Lyle said. "The emotions overtook me on the 1st tee. It's something I always dreamed of, having my daughter at a tournament. It was great she got to see what I do.
"My dream is to come here and make the cut. After 12 holes things were looking grim but I fought like crazy."
Scott was leading after the early groups finished, but was overhauled by Cullen, who fired an eagle on the 332-yard, par-4 11th and had six birdies but closed with a bogey at the 18th for a 65.
American Matt Kuchar opened with a 71.
