Åberg managed to play six holes in the third round on Saturday - and took two strokes off leader Robert MacIntyre - before play was suspended due to bad weather.
When the PGA Tour's Texas Open outside San Antonio resumed after an overnight suspension, the 26-year-old kept his composure and finished the third round tied for second at -13 overall, one stroke behind MacIntyre.
Åberg had about an hour to rest before heading back out to play the final round. He finished three strokes ahead of American JJ Spaun, who eventually won the competition. Åberg's total was -15, two strokes behind Spaun.
Alex Norén ended up in a tie for thirtieth place, at -7.
