Åberg shot 66 strokes, ten strokes better than on Saturday, to finish the year's third golf major at +3 overall and climb the leaderboard.
Åberg was tied for 21st when he finished his round, but there were still several hours of play left at Shinnecock Hills.
Play with Wyndham Clark (–7) and world number one Scottie Scheffler (–1) will kick off at 8:30 p.m., local time in Sweden.
