The Bees were in front after Ivan Toney opened his top-flight account in the seventh minute, but Emiliano Buendia equalised in the 13th minute.
Brentford end August with five points from three games and only one goal allowed while Aston Villa have a win, loss and draw through their opening three matches.
Story of the match
In a game that saw both sides trying to get on the front foot early, Brentford took the lead inside seven minutes. The goal came when a corner on the left was only cleared as far as Sergi Canos.
The wing-back took a touch and sent the ball in low, a flick from Pontus Jansson diverting it to Toney, who placed a shot past Emiliano Martinez and into the top corner.
Saman Ghoddos won possession in Villa territory looking to create a second goal. Toney was able to run at the defence, but he had his shot blocked.
Danny Ings started the build-up play that created Villa's equaliser. He ran in to the inside left channel and he held play up, playing a one-two with Anwar El Ghazi and picked out Buendía, who turned into space and let fly with a shot that David Raya got a hand to, but couldn't keep out.
Both teams had chances on set-pieces. Ezri Konsa flicked on a Buendía corner, and it took a vital clearance inside the six-yard box to stop a second Villa goal.
At the other end, Christian Norgaard almost got on to a long throw at the other end but Axel Tuanzebe got there just in time to prevent the Brentford midfielder from scoring from close range.
Martinez then denied Bryan Mbeumo after he got on the end of a Ghoddos pass and at the other end, El Ghazi's cross dropped for Ings that was brilliantly saved by Raya at point-blank range.
Just before halftime, Vitaly Janelt nipped the ball off Martínez when he tried to clear and rolled it home. However, it was decided that the German had prevented Martínez from completing a clearance, so the goal was chalked off.
The Bees should have been ahead after Janelt stepped into space, found Henry overlapping on the left and he cut across the ball a fraction and faded a shot past the far post.
Mbeumo then found some room, got by Matty Cash and although the Villa defender appeared to handle the ball, play continued and Mbeumo pulled his shot across the face of goal.
Ghoddos and Canos then had shots blocked as both teams chased a winner. The Villains had a chance when El Ghazi fired over and Brentford center-back Ethan Pinnock couldn't get enough power on his effort.
Late on, former Brentford man and Villa substitute Ollie Watkins failed to trouble Raya with a header, but he did force another fine save on a breakaway and that would ensure the game ended on level terms.
Man of the match: Emiliano Buendia
He opened his Villa account and created the opportunities for the hosts that, on another day, could have given them all three points.