In a thrilling finale, former world No.1 Webb came from five shots back at the start of the day to win by a shot from South Korea's Chella Choi after shooting a closing four-under-par 68 to finish at 12-under at Victoria Golf Club.
Seeking her first title, Choi (74) had a two-metre birdie putt on the last hole to force a playoff but pulled it to the left.
Australian teenage amateur Minjee Lee, who shared the lead with Choi heading into the final round, fell away with a 78 to finish five off the pace in a tie for 11.
It was a master class by 39-year-old Hall of Famer Webb, who has now claimed 40 LPGA Tour titles, as she secured her first Open crown since 2008.
The high of victory came after a career low last week when, as defending champion and eight-time winner, Webb was disqualified from the Australian Ladies Masters for signing an incorrect scorecard.
While others faltered in the gusty winds on Sunday, world No.8 Webb's class shone through as she held firm.
Playing six groups ahead, Webb had a nervous wait for Chella to complete her round.
Choi, who shot a course record 10-under 62 in her third round, started with a birdie but then hit her ball out of bounds on the second hole.
She followed that double bogey up with a bogey and couldn't buy a birdie from there, carding 15 straight pars.
Webb said she was delighted when she woke to see the wind blowing at the sand-belt course after three days of benign conditions because she felt it gave her a chance to catch the leaders.
"The course played completely different today and I hit some really good shots," she said.
"I made some really good putts at crucial times where it really kept my momentum going."
New Zealand 16-year-old Lydia Ko (73), France's Karine Icher (71) and American Paula Creamer (68) finished tied third at 10-under.
The American matched compatriot Gerina Piller and Webb in producing the round of the day.
World No.3 Stacey Lewis (69) tied sixth at nine under.