Clifford Miranda handed Dempo a first half lead, Ranty Martins scored a brace and Anthony Pereira was also on target as Dempo made it four points from two games in India's elite division following last weekend's 1-0 success over reigning champions Salgaocar.
Despite their eventual capitulation, Mumbai, 4-1 conquerors of Air India in their season opener, started positively, Sampath Kuttymani hitting the post early on with Dempo goalkeeper Subhashish Roy Chowdhury stranded.
Mumbai came close again soon after when Ebbie Sukoro's superb curled shot rebounded back off the crossbar.
Having survived those two early scares, Dempo could, and perhaps should, have broken the deadlock moments later, but Joaquim Abranches somehow failed to find the target when well placed.
Dempo finally went ahead in the 37th minute when Peter Carvalho tore the Mumbai defence to shreds, before playing a neat pass to Miranda who finished with aplomb. It signaled the end of Mumbai's resistance.
Within five minutes of the restart Martins doubled Dempo's advantage, the same player made it 3-0 in the 72nd minute before Pereira put the icing on the cake for Dempo with the fourth and final goal of the game.