That leaves Aberg tied for 17th, but still has some way to go to catch the leader, world number one Scottie Scheffler, who is sitting on -10 after two rounds.
After struggling with the windy conditions yesterday, Aberg got off to a much better start today with two birdies in his first three holes, in direct contrast to two bogeys in his first three yesterday.
Further birdies on the seventh and ninth followed, and despite a couple of bogeys on the back nine, both were either preceded or succeeded by a birdie.
That meant the 25-year-old completed one of the best rounds of the day four under par and two under for the championship.
Another Swede who showed improvement on day two was 2016 Open champion Henrik Stenson. Beginning the day at +4, he shot a -3 round of 68 to move to tied for 51st place.
Stenson is level with two of his compatriots - Sebastian Soderberg and Jesper Svensson, who shot round of -1 and +1 today. A three-over round for Jesper Sandborg has seen him drop back to tied for 99th and +4 for the championship, which will see him miss the cut.