Rafael Bastos scored in the sixth minute but the visitors failed to add to their tally as Goa's defence stood firm.
Sergio Lobera made just the one change from the first leg in Mumbai as Hugo Boumous started in place of Edu Bedia. The coach of the visiting side, Jorge Costa, brought in Milan Singh and Anwar Ali in place of Sehnaj Singh and Subhasish Bose.
Mumbai launched an attack though the centre early on as Arnold Issoko skipped past Ahmed Jahouh and set up Bastos in the box who put his team in the lead.
Brandon Fernandes and Boumous worked a good one-two in the Mumbai box in the 21st minute but Mumbai defender Lucian Goian's timely interception prevented damage.
Goa's only shot on target in the half was Brandon's second-minute free-kick that landed in the hands of rival goalkeeper Amrinder Singh while Boumous also saw his header from Jackichand Singh's cross from the right go wide in the 38th minute.
Jackicand's cross from the right was punched away by Amrinder Singh but it fell for Ferran Corominas whose shot hit the crossbar. Both teams had chances after the break but Mumbai, who desperately needed to score more goals, failed to convert.
Issoko then tested Naveen who made a comfortable save in the 65th minute. Minutes later, the Goa custodian put his body on the line to deny Bastos from close range following a failed interception by Seriton Fernandes.
Modou Sougou and Matias Mirabaje went close at the fag end but a miracle was improbable by then.