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Djokovic absorbed a barrage of powerful hitting from Canadian Denis Shapovalov to move on step closer to a record-equalling 20th Grand Slam title.
Bopanna and Shapovalov recorded a 4-6, 6-4, 6-3 win over German duo Kevin Krawietz and Andreas Mies in a match that lasted an hour and 47 minutes.
The 20th seed, who is eyeing a place in his maiden Grand Slam final, will face Alexander Zverev Zverev in the last four.
The Indian-Canadian pair suffered a 5-7, 5-7 defeat at the hands of Rojer and Tecau in the quarterfinals. The loss also ended the Indian challenge at the Grand Slam.
Shapovalov, 20, needed just 70 minutes to brush aside world No. 7 Zverev, who lost his third straight singles before the year's first Grand Slam starting in Melbourne on January 20.
It was Djokovic's fifth victory over the 20-year-old Canadian in as many clashes but by far the toughest, after Shapovalov controlled significant portions of the match played in Australia's intense summer heat.
Results 1-6