While Jayaram beat Marius Myhre of Norway 24-22 21-5, Bhat, seeded 13th, outplayed compatriot Kirtesh Dhindhwal 21-16 21-12 to enter the third round of the men's singles event.
But all other Indians -- Anand Pawar, R M V Gurusaidutt, Chetan Anand -- lost their respective men's singles second round matches to crash out of the tournament.
In the women's singles also, the lone Indian representative, Sarada Jasti went down fighting 21-18 17-21 17-21 to a qualifier, Vicki Copeland in the opening round.
Bhat had an easy outing against qualifier Dhindhwal, who he beat in just 23 minutes. Bhat will take on sixth seed Andre Kurniawan Tedjono in the next round.
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It was an off day for Pawar but Chetan and Gurusaidutt fought hard before losing their respective ties.
Pawar, fifth seed, was thrashed by unseeded Chia-Hsin Wan of Chinese Taipei 16-21 14-21 in 36 minutes.
Fourteenth seed Chetan conceded the first game advantage to go down 21-17 17-21 12-21 to Parinyawat Thongnuam of Thailand in a match that lasted 56 minutes.