Hall, who was leading with five holes to play, bogeyed the 16th and missed an eight-foot birdie putt for the win, while Pedersen sunk two birdies in her last five holes to force the playoff after both players ended tied on 10-under par.
Pedersen birdied the first extra hole to claim her third Ladies European Tour (LET) crown after her victories at the Indian Open in 2015 and the Czech Open in August.
"It's very special," Pedersen said. "I'm very happy that I got to be the first person to win a tournament here and I think it's great we're playing here. The country has a bright future in golf and hopefully we'll be back for many years.
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"I'm really proud that I got it back twice, I feel like I was out of it at the start of the front nine, then again at the start of the back nine but I kept fighting back."
The victory extended Pederson's lead in the Race to Costa Del Sol standings, the tour's Order of Merit.
The event at the Royal Greens Golf & Country Club was the first professional women's golf tournament to be held in Saudi Arabia and the third-highest paying LET event after the British and Scottish Open, with a total prize purse of $1 million.
Sweden's Caroline Hedwall finished third on eight under, one shot ahead of Dutchwoman Anne van Dam and Stephanie Kyriacou of Australia.
The Saudi Ladies Team International, where professionals will team up with amateurs and compete for a $500,000 purse, will be held at the same venue from Nov. 17-19. (Reporting by Manasi Pathak in Bengaluru, editing by Pritha Sarkar)
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