The Bees looked to be cruising home with an away victory – thanks to Neal Maupay’s double – but the Cote d’Ivoire ensured his side got a point with his late seconds strike.
The Villans continued their unbeaten run after holding Ipswich Town to a 1-1 draw on Saturday.
But against Brentford, they made a false start with Maupay giving the visitors the lead in the 23rd minute courtesy of a thunderous half-volley thanks to an assist from Ollie Watkins.
With six minutes left to play in the first half, Kodjia’s fine solo effort got his side the equaliser.
In the 82nd minute, however, Maupay completed his brace to put Dean Smith’s men in line for a shock away victory.
And with ten seconds left in the cracker, Kodjia buried a header that sent Villa Park into blisses.
Aston Villa are fifth in the English Championship log. They host Reading in their next game with the intention of maintaining their unbeaten run.