The ISL side put past three with the help of Ogbeche (6'), Akash Mishra (45'), and Javier Siverio (68') whereas Rajasthan United FC managed to equalise with a goal from Martin Chaves (29', P) but it was too little to make any difference.
While Scottish player Greg Stewart (40', 100' 118') got a hat-trick, former Chennaiyin player Lallianzuala Chhangte (78', 94') scored a brace for Mumbai City.
Both sides shared a similar fate in the group stage as the Islanders collected seven points from four games and topped their group while the Marina Machans picked up as many points and finished second in their group.
Chennaiyin FC beat I-League sides TRAU FC and NEROCA FC 4-1 and 2-0 respectively to finish second in Group C after a poor start and qualify for quarter-finals
Both teams have taken contrasting routes to reach the knockouts. While BFC played all their games in Kolkata and won three out of four to qualify in as Group A second place holders, OFC won all their four games to qualify as Group D toppers from the Guwahati leg of the tournament.
Midfielder Anirudh Thapa (15') and Vafa Hakhamaneshi scored in each half to take Chennaiyin FC past the hosts and into the knockout stage of the competition.