Villa took the lead through Watkins in the 85th minute after Alex Moreno responded to Keane Lewis-Potter had put Brentford ahead earlier in the contest at the GTech Community Stadium.
Watkins, who spent three years with the Bees, reacted the quickest by nodding in from a free-kick and immediately celebrated by pointing to the crowd while in the goal.
He then put his hands on his hips as his teammates celebrated with him.
That infuriated the Brentford players, including Saman Ghoddos, who tried to pull them out of the goal.
It led to a fracas as more players got involved, leading to a goalmouth scramble.
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Ghoddos was booked for his role in the melee, as well as Ezri Konsa, who is also a former Brentford player.
The fury continued later in the match, which finished 2-1 to Unai Emery's side, with Villans midfielder Boubacar Kamara being sent off in stoppage time for pushing Yegor Yarmolyuk in the face.
It means that Villa will likely now be without the Frenchman for three games, which includes a trip to Old Trafford to take on Manchester United.
Nevertheless, this was a vital three points for Emery with his side now flying up to second in the Premier League before Liverpool face United.
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They sit a point behind league leaders Arsenal and might even consider themselves as title contenders this season.
But it could have been different had Brentford held firm after going a goal up through Lewis-Potter on the stroke of half-time.
Ben Mee was shown a straight red after a high challenge on Leon Bailey with VAR intervening in the 71st minute and moments later, Villa had their equaliser.
Alex Moreno's bullet header saw them grab the equaliser before Watkins gave Villa the winner.
His celebration did not go down well with the Brentford fans, though, as he pointed to the crowd.