Muster, 28, took home $315,000 for the first indoor title of his career Sunday.
The Austrian, who is ranked No. 3 in the world, has won 35 career titles, 33 on clay and one on a hard court.
Muster beat second-ranked Pete Sampras in the semifinals of the $2.1 million tournament. The field included 20 of the top 22 players in the world.
Washington, 24, was unseeded but beat top-ranked Andre Agassi.
Agassi will miss this week's Paris Open because of a chest muscle sprain and as a result will relinquish the No. 1 ranking to Sampras at the end of the week no matter how Sampras does.
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