It was Levy’s first title since the 2014 Portugal Masters.
Fisher, champion in 2008, hit a 64 on Sunday to set up the playoff after Levy, who went into the final round with a four-shot lead, had bogeyed his final hole.
Europe's Ryder Cup member Martin Kaymer shot a 68 to finish sixth on 14-under, five off the lead, on home soil.
Levy breathed a sigh of relief after winning the title, having carded bogeys on three of his first five holes on Sunday and again on two of his final three holes.
"I definitely feel very relieved because it looked like I had lost my chance. It’s so good to have this winning feeling again after two years, it’s very nice," the 26-year-old told reporters.
“I came close last week in Italy (after finishing in a tie for seventh at the Italian Open) but didn’t play well on Sunday. So this week, it feels great to have this trophy in my hands.
"It was tough to try to hold on to a four-shot lead. I didn’t play well on the front nine. I was thinking about the score and not on my own game.
"But I stayed patient and I started to play really well on the back nine, and in the end it worked out well.”
(Reporting by Pritha Sarkar, editing by Ken Ferris)
