Åberg shot 66, ten better than on Saturday, after five birdies and only one bogey.
The winds were kinder than earlier in the week and Åberg made the most of it. He was one of three players who had the best round on Sunday at the difficult Shinnecock Hills.
It was enough to climb to a tied for 17th place with a total of three strokes over par.
"It's nice to end in a nice way," Åberg told Viaplay.
"Then of course there are some things, especially Friday and Saturday, that I would like to do again."
Wyndham Clark, USA, held off and won at -4, one stroke ahead of compatriot Sam Burns.
Ludvig Åberg also competes in Connecticut next week, before the 26-year-old golf star heads home to Sweden for a week of rest. After that, the Scottish Open awaits, followed by the British Open, the last major of the year, which is played at Royal Birkdale.
