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The victory confirms the 20-year-old as a member of tennis' new generation of men's players who can challenge the game's long-dominant players.
Wimbledon finalist Anderson took a medical time-out mid-way through the four-set match before becoming the highest ranked player to be ousted from the first major of the year.
The world number one was immaculate from start to finish against the 32-year-old as he put himself within touching distance of a record-equalling sixth title at the year-ender.
The 37-year-old shrugged off the passing of time to swagger past the dangerous Anderson 6-4, 6-3 and reach the semi-finals.
The Serb was back roaring into the skies in triumph as he captured a 13th Grand Slam title to end a 25-month barren run at the Slams.
History books will show that Anderson came out on top in a 7-6(6), 6-7(5), 6-7(9), 6-4, 26-24 epic that lasted six hours and 36 minutes .
The Swiss eight-time champion and top seed was beaten 2-6, 6-7(5), 7-5, 6-4, 13-11 by eighth-seeded Anderson before a stunned crowd.