Levy had a big lead heading into the final day of the tournament, having shot a round of nine-under par yesterday, but the Frenchman's six-over 78 today saw him slip back into the chasing pack.
Siem and Fisher both carded rounds of 67 to move level with Levy at the end of the fourth round.
Fisher and Levy appeared to have the edge at the start of the playoff as they both found the green with two shots, while the German's approach shot sat at the edge.
However, Siem managed to chip the ball in from just off the green to leave his opponents needing a birdie to keep themselves in contention.
The Englishman pulled his putt to the right of the hole, while Levy's effort from 12 feet also missed as Siem clinched his fourth victory on the European Tour.