Bhupathi, who gave the Asian Games in China a miss to play in the season-ending USD 5,070,000 ATP event, and Mirnyi won 7-6(2), 6-4 over the pair of Poland's Kubot and Australia's Marach.
The third-seeded Indo-Belarussian combination, who had won the ATP World Tour Masters 1000 Paris title eight days ago, needed one hour and 33 minutes to win the Group B round-robin match.
Bhupathi and Mirnyi targeted Kubot's forehand right from the start, but the Indian had his serve broken in the third game when a Kubot return hit the net -- evading the long reach of Mirnyi -- only to land inside the baseline.
Bhupathi redeemed himself on Marach's serve at 4-3, when, after a long baseline rally, the 36-year-old Indian hit a powerful forehand winner off a lob.
The third seeds went on to seize control of the tie-break by opening up a 4-1 lead and eventually clinched the 50-minute opening set. The duo hit three aces and four double faults, but Mirnyi's net play made the difference.
Sixth seeds Kubot and Marach soon found themselves in trouble in the second set at 1-1. A Bhupathi lob on Marach's serve allowed Mirnyi to cross the net for a fine forehand winner down the middle that pierced the Polish-Austrian pair.
Bhupathi and Mirnyi, who appeared at the year-end championships in 2003 and 2004, grew in confidence and maintained the service break advantage to take the second set and win the match.
Bhupathi has won at least one ATP World Tour title for 14 straight years (since 1997) and 33-year-old Mirnyi has captured at least one title for 12 consecutive years (since 1999).