Brentford started brighter, opening the scoring after seven minutes when Ivan Toney found himself unmarked in the box and fired home an unstoppable strike following a low cross from the left by Sergi Canos that was flicked on by Pontus Jansson.
Villa hit back six minutes later through Emiliano Buendia after smart work by Danny Ings on the left, the new signing feeding the ball on the edge of the box to the Argentine who finished emphatically.
The second half started much like the first, with both teams taking the game to each other though clear chances were hard to come by.
The match got a bit feisty towards the end as both sides desperately searched for a winner, with six players seeing yellow cards -- three for each team.
For Villa, a major cause of concern came with an injury to central defender Ezri Konsa, who was forced off due to a knee problem just before the final whistle.
"I am reasonably satisfied," Villa boss Dean Smith said."We lacked a little bit of quality and fluidity in the final third and that cost us the victory. I am disappointed with the way we conceded but pleased with the way we came from behind."
Brentford manager Thomas Frank was happy with how his side started each half but asked them to play with more courage.
"Happy with most of the performance. We started the game brilliant at a difficult place to play. We scored and I felt we were really on top of the game. Then one miscommunication and it gave them the chance," he said.
"I would like us to be even braver. My message before every game is to go for a win, play forward and attack. I just probably need to keep reinforcing it."
The draw leaves Villa in 11th place on four points from three games, with Brentford two spots higher on five.