Ireland's Lowry, who won the Irish Open as an amateur in 2009, carded a final-round 66 to edge out England's Fisher, who bogeyed 16 and 18 for a 70.
Fisher, hunting his first win since 2010, had a five-foot putt at the last for a play-off but his ball lipped out.
Former US Open champion Michael Campbell finished third.
"I can't explain how I feel now to be honest. It's a dream," said Lowry, 25, who is only the second player to win on the European Tour as an amateur and a professional after Spain's Pablo Martin.
"I've won such a big tournament, such a prestigious event. I'm over the moon. It was like playing in Ireland [given the fans' support], it was great."
Lowry, a stable-mate of world number one Rory McIlroy, holed a seven-iron for an eagle two at the 11th and was one ahead after adding birdies at the 15th and 17th.
But he drove into sand at the last before making bogey for a 14-under-par total.
Former Ryder Cup star Fisher, who was in the final group, left his long birdie attempt at 18 five feet short and was unable to make the follow-up.
New Zealand's Campbell finished on 12 under, his best finish for four years and a welcome result after years of struggle since winning his only major in 2005.
Overnight leader Bernd Wiesberger of Austria had to settle for fourth after a 73 left him on 11 under.
