Aberg moved ahead of Harris English and Viktor Hovland on Thursday (Friday AEST) with an 8-iron to about 15 feet on the back corner of the green on the par-3 17th and made the birdie.
Houston Open champion Gary Woodland, Matt Fitzpatrick and Rickie Fowler were in the group of players at 65 to share fourth.
New Zealand's Ryan Fox and Americans Andrew Novak and Michael Brennan also shot 65 on the opening day.
Masters champion Rory McIlroy skipped this $20 million (AUD28 million) signature event for the second successive year, having said Harbour Town doesn't suit him.
Jason Day, Karl Vilips and Min Woo Lee are the only Australians in the field and all shot an opening-round 70 to be tied for 44th.
Scottie Scheffler, the runner-up last week at Augusta after a 65-68 finish, had a shocking start. His first tee shot was out-of-bounds on the right. He didn't know out-of-bounds was over there.
"It was looking like it was going to hit those trees and I guess it flew right through them and then hit path and went out-of-bounds," Scheffler said. "Thumbs up for the start. It was a good bogey."
That it was, a 12-foot putt to limit the damage, followed by a par save on the next hole and then it was business as usual in the tougher afternoon conditions for a 68.
Aberg had a disappointing week at Augusta National by his standards, finishing in tie for 21st which was his first time out of the top 10 in three appearances at the Masters.
"I felt like I was playing well but made some silly mistakes that prevented me from having a real chance," Aberg said.
"But I also felt like in the grand scheme of things, I was swinging it nice, I was moving it nice, so I didn't have to prepare that much in terms of my golf swing on Monday through Wednesday, and I felt like good golf was in there."
