Fox began the day three shots behind overnight leader Aberg and a triple-bogey seven on the third hole appeared to have taken him out of contention.
But the 36-year-old covered his last 13 holes in eight under par for a closing 67.
Fox's 18-under-par final total gave him a one-shot victory over playing partner Aaron Rai and Tyrrell Hatton.
"I don't really know what to think at the moment to be honest," Fox said after his fourth DP World Tour title.
"It's not a tournament that has treated me very well in the past, although I've loved coming here. I don't know what changed today but it's pretty special to make a birdie on the last to win.
"To have a back nine like that, especially after how I started the day, it's amazing. I played great and pretty much didn't miss a shot from the third hole onwards."
Rai missed a long eagle putt on the 18th which could have given him the title or at least forced a play-off.
World number three Jon Rahm, who had been runner-up on each of his two previous appearances at Wentworth, carded a 68 to claim fourth place on 16 under.
Sweden's Aberg, who had been seeking successive tournament victories in just his 10th event as a professional, held a two-shot lead after 54 holes.
But the 23-year-old sensation slumped to a closing 76, including two double bogeys in the space of three holes.
'Stupid mistakes'
Aberg, whose victory in the final qualifying event earned him a Ryder Cup wild card, admitted failing to close out victory would "sting for a long time".
"It was quite difficult out there and I made a few stupid mistakes where I missed on the wrong side and was a little bit too cute with the chips," he said.
"It cost me today and I'm trying to learn from it. I'm looking forward to the next time I'm in that same position."
Seven members of Europe's Ryder Cup side packed the top 10, with Rory McIlroy surging through the field with a round of 65.
McIlroy, who only made the cut thanks to a birdie on the 18th hole in near darkness on Friday, finished in a tie for seventh place before heading to Mykonos for a friend's stag do on Monday.
Asked if Europe captain Luke Donald would be pleased ahead of the clash with the United States in Rome later in September, McIlroy said: "It's awesome. We're in a good spot.
"We had a really good day in Rome on Monday, the team's been shaping up really well for the last couple of months, everyone's been in pretty good form.
"It's still almost two weeks away until the first ball is hit on the Friday morning but I'm sure you'll ask all the boys that are coming in here they are all just so excited to get to Rome and get going."
