Pospisil, seeded seventh, beat Bedene just over two months ago indoors in Valencia, but the closely ranked pair virtually went point for point outdoors in Chennai. Bedene earned the only break.
He was runner-up here last year as a Slovene, and returns as a Brit after becoming a citizen in March.
Russian teen Andrey Rublev, a wild card, beat local qualifier Somdev Devvarman 6-3, 3-6, 6-3 for a shot at two-time defending champion Stan Wawrinka. Also the top seed, Wawrinka is aiming for a fourth Chennai title.
Second-seeded Kevin Anderson of South Africa also learned of his next opponent, 248th-ranked wild card Ramkumar Ramanathan, who beat Daniel Gimeno-Traver of Spain 6-2, 6-0 for his second career win on the ATP Tour.