Aberg birdied four of the last six holes at Torrey Pines to complete a final round of 66 and finish 12 under par, a shot ahead of American Maverick McNealy.
Aberg, who had covered the front nine in 34, still need a strong finish to force himself into contention and duly birdied the 13th, 14th and 15th before two-putting from 70 feet for birdie on the par-five 18th.
The 29-year-old had to hole from 38 feet to save par on the first, but birdied the next five holes in a row and picked up another shot on the ninth to reach the turn in 30.
McNealy had set the clubhouse target following a closing 64 but ultimately paid the price for covering the last five holes in one over par.
Further birdies on the 10th, 11th and 13th briefly gave McNealy a three-shot lead before he dropped his only shot of the day on the 14th after failing to get up and down from a greenside bunker.
