Pepperell carded a closing 70 at Doha GC to finish 18 under par and a shot ahead of playing partner Fisher, who missed from 10 feet for birdie on the last to force a play-off.
The pair began the day tied for the lead but Fisher's chance looked to have quickly disappeared when he bogeyed three holes in a row from the fourth, with Pepperell following eight straight pars with a birdie on the ninth.
However, Fisher rallied superbly with five birdies on the back nine, including a tap-in on the par-three 17th to close within a shot of the lead.
Pepperell was unable to birdie the par-five 18th after laying up into the rough, but Fisher's own birdie attempt swung agonisingly across the hole.
A relieved Pepperell told Sky Sports: "I need a glass of wine and more than that I think! What a day.
"Oli made it really tough and I made it tough for myself at the end there with the second shot on 18. I felt good all day, I was in a great place mentally and kept telling myself I'm going to win this and Oli certainly made life more interesting.
"Relief I guess is the number one emotion, as is always the case with a win - although I haven't had many. I guess it will give me that confidence. I've always believed I would win out here but it hadn't happened before today. You have to take that step and it's not easy but hopefully this is not my last."
Pepperell, who began working with a new coach recently, held a three-shot lead after his second birdie of the day on the 10th, but enjoyed a major stroke of luck when his approach to the 12th bounced off the rocks short of the green and allowed him to save par.
Pepperell, who chipped in for a bogey on the same hole in round three after hitting the rocks three times, joked: "They can bomb (that hole) if they want.
"Me and Mick (Doran, his caddie) did joke walking off the green we'd be happy never to see to that hole again."
Fisher, whose sole European Tour win to date came in the 2011 Czech Open, told European Tour Productions: "It went all the way to the last hole, which I guess after my front nine is what I was hoping for.
"I hit a lot of good shots on the back nine but just made too many bogeys today. I made four bogeys and you're never going to win a tournament making that many mistakes on a Sunday, but at least I pressed him all the way. It's not the result I wanted but there was some good stuff there."
Sweden's Marcus Kinhult carded a closing 68 to finish third on 16 under, with Renato Paratore, Pablo Larrazabal, Gonzalo Fernandez-Castano and Gregory Havret all a shot further back.
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