A 4-0 victory earned the Delhi team a meeting with Garhwal Heroes in the Durand Cup football tournament qualifiers.
Eugenson Lyngdoh had found the net in the 32nd minute for the hosts but Rafael Coelho Luiz (34) and Jonatan Lucca (44) brought FC Goa back into the game. Mutu (90+4') scored the late equaliser to salvage a point for Pune City.
This was Dynamos' second win in three outings, while Pune suffered their first defeat at home at the Balewadi Stadium.