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The 43-year-old Bopanna, coming out to play his 33rd and final tie, and Bhambri raced to a 6-2, 6-1 win over Elliot Benchetrit and Younes Lalami Laaroussi.
Ankita, Rutuja progress to pre-quarterfinals
They lost in straight sets to top seeds Wesley Koolhof of the Netherlands and Great Britain's Neal Skupsk in the semifinals.
Overall, Bopanna, a US Open runner-up in 2010, has made four Grand Slam semifinals in the men's doubles
The Indo-Australian duo defeated Stalder and Pel in a pre-quarterfinal that lasted two hours and 19 minutes.
Sania also termed the day she and Bopanna lost the bronze medal match in the Rio Olympic Games in 2016 as 'one of the worst days'of her life.
But the Karnataka player won't be able to play his farewell match in his home state, as desired by him, since the All India Tennis Association has already awarded the match to Uttar Pradesh.
Bopanna and his partner Matthew Ebden of Australia beat the top-ranked pair of Dutchman Wesley Koolhof and Briton Neal Skupski 6-3, 2-6, 10-8 to claim their second title together and first of the season.
India lost the tie 2-3 on Saturday with Holger Rune starring for Denmark.
Unseeded Bopanna and Sania lost 6-7(2) 2-6 to Brazilian pair of Luisa Stefani and Rafael Mataos in the final at Rod Laver Arena.
Results 21-30 of 54