The reigning V.League 1 champions had suffered a 3-1 defeat to Ninh Binh in their last league outing, but Phan Thanh Hung's charges bounced back in superb style at the Shree Shiv Chhatrapati Sports Complex.
Pune had lost three of their last four I-League matches, yet the hosts held their own in the first half as neither side could break the deadlock.
It took just seven minutes for the visitors to take the lead after the break, however, as Sam Gallagher rose highest to head home Pham Thanh Luong's corner.
Mustapha Riga had the opportunity to level for the hosts shortly after the hour mark, but he failed to hit the target.
Ha Noi duly punished the former Bolton Wanderers man's profligacy, as Nguyen Van Quyet headed home Hughton Hector's cross on 71 minutes.
The match was put beyond doubt in the 83rd minute thanks to Hector's neat finish with the outside of his left boot, as Pune's maiden Champions League appearance came to an abrupt end.
Ha Noi can now look forward to a second round qualifying contest with Thai outfit Muang Thong United, who finished second in last season's Thai Premier League.
