Paes has 5575 ranking points, while Bhupathi lost a spot to slip to eighth with 5015.
Paes had made the quarter-finals of the Australian Open men's doubles event with Czech Lukas Dlouhy. He clinched the mixed doubles' championship on Sunday with Zimbabwean Cara Black.
Bhupathi, on the other hand, had a forgettable outing at Melbourne Park, losing in the very first round of the men's doubles event due to a calf muscle injury.
The veteran later pulled out of the mixed doubles' event in which he was to team up with compatriot Sania Mirza.
Sania, meanwhile, also slipped down three rungs to 59th following her second-round exit from the Australian Open.
The Hyderabadi, who recently broke off her engagement with childhood friend Sohrab Mirza, however, rose five places to 33rd in the doubles' chart.
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Paes reaches QFs of men's doubles, mixed doubles