Mumbai to Goa!Dubai to Goa Flights
Air India (AI 994) flies direct non-stop to Goa (GOI) from Dubai (DBX). This is the fastest (and cheapest too!) to fly to Goa direct from Dubai. This is a late night flight.
Air India (AI 984) flies direct to Goa via Mumbai, with 1 hour stop at Mumbai (MUM). It's a 5 hours flight from Dubai to Goa. Probably that's the next fastest way to travel from Dubai to Goa.
All other alternatives include a change of flight. Check out one of the Dubai to Mumbai flights. There are quite a few daily flights from Dubai to Mumbai. So is the domestic connection frequency between Goa and Mumbai.
Also keep in mind the hassles of changing from the international terminal to the domestic terminal at Mumbai, from where the Goa flights operate. It's a 1 hour+ affair, at least includes a bus transfer.
Another smart alternative is to fly from Sharjah (SHJ) to Goa. There is an Air Arabia flight (G9 492) that flies direct from Sharjah (SHJ) to Goa (GOI). It's a 3 hour flight to Goa.