Levy led the field by four going into the third and final round of an event dogged by disruption due to fog and curtailed to 54 holes.
Sweden's Michael Jonzon led the chasing pack but it was Fisher, one shot further off the pace in third, who emerged as Levy's greatest danger.
Fisher picked up four birdies on the front nine as Levy for the first time this week dropped shots at the first five holes.
Levy led his playing partner by one shot standing on the final tee, but a closing bogey forced a play-off.
The pair went back to the 18th tee and after both parred the hole Levy produced an 18-foot birdie putt at the second attempt to seal his third European Tour event.