Mumbai's hopes of entering the semis came to an end at the Jawaharlal Nehru Stadium after Stiven Mendoza (9'), Jeje Lalpekhlua (17') and Bernard Mendy (45'+2') found the net to seal three points for the hosts.
With rains lashing the stadium here, both Mumbai and Chennai had to deal with the tricky conditions. Just nine minutes into the match, Mendoza scored the first goal after Zakeer Mundampara played him through on goal for the Colombian to score.
The hosts doubled the lead eight minutes later when Thoi Singh guided Dhanachandra Singh's cross straight into Lalpekhlua's path for the 24-year-old to score his third goal in his last two games.
Mendoza could have made it 3-0 but for Mumbai goalie Subrata Paul, who managed to put him off. Midway through the first half, Raphael had to be substituted as he pulled his hamstring and Manuele Blasi replaced the Brazilian in midfield.
The Colombian set up Thoi Singh near the half hour mark with another brilliant pass but Singh's shot was off target. Chennai had another golden opportunity to get their third goal three minutes before half-time when Mendoza was played through with just the keeper to beat.
Paul once again came to Mumbai's rescue to deny Mendoza his second of the night. When they did eventually get their third, it came from one of the unlikeliest of sources in Mendy who scored his second of the season.
Thoi Singh once again threaded through a picture-perfect pass which Mendy ran onto before chipping it over Paul to make it 3-0 at the stroke of half-time.
The visitors made a brighter start to the second half with Sony Norde forcing Apoula Edel into a save. Norde then set up substitute Selim Benachour in the 64th minute but the Tunisian sent his effort high above Chennai's crossbar.
Norde tested Edel once again 12 minutes from full-time but the Armenian keeper was alert to the danger as he saved the Haitian's initial effort before clearing the ball with his feet to keep his clean-sheet.
The last chance of the game fell to Sunil Chhetri who rattled Chennai's post as the game ended 3-0.