The 25-year-old Lowry, who won the 2009 Irish Open as an amateur, scooped his first victory as a professional after shooting a 66 to finish one shot clear on 14-under-par for the week.
Lowry started the day four shots off the lead but sizzled around the Oceanico Victoria course on the Algarve, holing an eagle two at the 11th.
However, he bogeyed 18 after finding sand to give Englishman Fisher the chance to win outright with a birdie on the last or take the battle into a playoff with a par.
The 2010 Ryder Cup player left himself with a monster putt for a three and his four-footer for a par popped out of the hole to prompt wild celebrations from Lowry watching on a big screen from the range.
"I can't explain how I feel now to be honest. It's a dream," he told Sky Sports.
"I've won such a big tournament, such a prestigious event. I'm over the moon. It was like playing in Ireland (given all the fans), it was great."
Overnight leader Bernd Wiesberger of Austria had to settle for fourth after a 73 left him on 11-under while New Zealand's Michael Campbell finished third on 12-under as the 2005 U.S. Open champion found some rare form after years of struggle.