In the end, it turned out to be an easy victory to Sergio Lobera's side, who are now at the top of the ISL table.
Ferran Corominas (45+1), Manuel Lanzarote (45+3), Adrian Colunga (85th) and Manuel Arana (88th) registered their name on the scoresheet for FC Goa.
For Delhi Kalu Uche score one goal which was no more than a consolation for the home side.
After both sides rattled the bar early on in the first half, FC Goa opened the scoring in a bit fortuitous fashion.
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Almost immediately after the restart, Delhi conceded again. Having contributed to the first goal, Lanzarote smashed in a 30-yard curler to double the advantage for Lobera's side just before the referee blew the whistle for half-time.
In the second half, Delhi Dynamos started off brightly and, at the hour-mark, Delhi pulled one back.
Uche's strike looked to ignite a comeback for Delhi but all their hopes were doused in the 66th minute when Gabriel Cichero was given marching orders by the referee after the Venezuelan picked up a second yellow.
Even after Cichero's dismissal, Delhi worked hard but an own-goal by Pritam Kotal in the 84th minute opened the floodgates for FC Goa who hit two more goals to stun the home fans.
In the 88th minute, Arana, who had provided an assist earlier, latched on to a loose ball in the box to slam home Goa's fifth of the night.