Bopanna is behind world's most formidable players, American twins Mike and Bob Bryan.
Bopanna moved up as Spaniards Marc Lopez (4) and Marcel Granollers (5) lost a place each.
After his Wimbledon semifinal appearance, Bopanna had become country's highest ranked player at number five.
This week Mahesh Bhupathi lost a place to be number seven while Leander Paes is static at nine.
Divij Sharan also achieved a career-best rank of 66 with a jump of 18 places, courtesy his title win at Claro Open with Purav Raja.
In the singles, Somdev Devvarman continued to be highest ranked player at 128, followed by Saketh Myneni (263).
In the women's doubles, Sania Mirza moved up to 17th from 19th.
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