He got off to the ideal start making an eagle-3 at the par-5 first and never relented despite a bogey at No. 3.
Fisher finished off Saturday's third round with four birdies in a row to post a seven under par 65.
Adrian Otaegui began the day in the lead but is now five shots back after a disappointing 73.
On the last, Pepperell laid up with his second into the thick rough, made wet and unwieldy by rain in the Qatar capital, but found the green in three and two-putted for the win when Fisher missed his birdie putt. We've still got one round to go but I've certainly put myself in a good position.
"I am looking forward to it", Pepperell said. Many labeled the gregarious 27-year-old a rising talent on the European Tour, but he needed 129 starts in six seasons (along with one return trip Qualifying School) before finally claiming the breakthrough win so many expected. "I'm good friends with Eddie so hopefully we'll have a bit of fun out there", he said.
"I hit a lot of good shots, I maybe lost a little feeling through the turn, but I bounced back nicely and I didn't let it bother me".
"It went all the way to the last hole which, after my front nine, was what I was hoping for on the back nine", said Fisher, who won the 2011 Czech Open, but recorded his first top-three finish since the 2014 Africa Open. "I didn't want to be behind the leader".
Also in the running are a group of five players on twelve under par, including Sweden's Marcus Kinhult and France's Gregory Havret.
England's David Horsey is among those chasing the leaders on 12 under in joint fourth place, with fellow English pair James Morrison and Chris Wood a further shot back.
The English duo held a share of the lead heading into the final round at Doha Golf Club, but it was Pepperell who was crowned champion under pressure from Fisher in a tense finale.