Wawrinka, winner of three Grand Slam tournaments, trailed by two sets overnight, having squandered set points in the opener, but led 6-5 in the third when play resumed in muggy conditions.
He then had two set points in the tiebreak but missed both, spraying one backhand well wide, and the 29-year-old Fabbiano completed the best win of his career.
"I'm really disappointed to lose a match like yesterday and today. I think I was playing really well yesterday," unseeded Wawrinka, who took out sixth seed Grigor Dimitrov in the first round, told reporters.
"I had a lot of set points in the first set. Set points again today. Could have changed a lot. Unfortunately I lost in three sets."
Since reaching least year's French Open final Wawrinka has tumbled down the rankings from three to his current 224, mainly as a consequence of the knee surgery he required last year.
He lost in the first round of the French Open this year, the second round in Australia and at last year's Wimbledon he was knocked out in round one. He did not play the U.S. Open.
While in the early part of the year Wawrinka was still troubled by his knee, he said the problem now was more a matter of restoring the self-belief missing from his game.
"I've been pushing myself, pushing my body. I think my level is there. Now it's about getting back the confidence, winning some tough match, finding a way how to win those points like the set point yesterday," the 33-year-old said.
"Those little things can change a tournament."
Fabbiano, ranked 133rd, goes on to play Greek Stefanos Tsitsipas in the third round with both men looking to reach the last 16 of a Grand Slam for the first time.
(Reporting by Martyn Herman; editing by Clare Lovell)
