Aberg, who equalled his highest world ranking of fourth earlier this month before dropping back to sixth, was one of the first out on the course.
Beginning on the back nine, the supposed gentler half of the tough course in Pennsylvania, Aberg began with two birdies before a bogey on the par-four 12th. He followed that with par on the next five holes before a birdie on the 18th to be on two under par halfway through his round.
But the front nine lived up to their tricky reputation for the 25-year-old, who bogeyed the first, and though he birdied the third, back-to-back bogeys at the fifth and sixth took his overall score to level par.
A strong finish would put him right back among the leaders, but the 2024 Masters runner-up bogeyed his final two holes, to finish the par 70 course at +2.
As he finished, Aberg was tied for 16th, with only a handful of players below par.
Compatriot Joakim Lagergren had a more difficult afternoon at Oakmont, finishing his opening round on 10 over par.
Having begun with four pars, the world number 185 followed up with two bogeys and one double bogey in his next four holes, before recording the only birdie of his round to finish the back nine at +3.
Another double bogey on the par-four second only worsened his afternoon, before five more bogeys on the last seven holes meant he finished on +10.
At the time of writing, Lagergren is tied for 141st, while Aberg is tied for 65th, with many players still out on the course and some yet to tee off. The USA's JJ Spaun currently leads and is in the clubhouse at -4.