Graf, the world No 2, put the top seeds on their way towards victory with a 6-4, 6-3 defeat of Arantxa Sanchez Vicario and then Stich gave them an unbeatable 2-0 lead with a straight sets win in the men's singles over Arantxa's older brother, Emilio.
The German victory was particularly satisfying for Graf, who was weakened by a virus in last year's event which contributed to a semi-final defeat with Boris Becker, and later forced her withdrawal from the Australian Open.
Graf had failed in two previous attempts to win the Hopman Cup, one of the few titles to elude her in a glittering career. She twisted her right ankle against France in the semi-final, but received treatment before the final and did not appear to be hampered. As a precaution, the Germans forfeited the meaningless mixed doubles as Graf did not want to aggravate the injury before the Australian Open, which starts on 18 January.
'It started hurting in the second set, there are a few problems with the ligament and it needs a few days' rest,' Graf said.
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