Goals from Mohamed Salah, Diogo Jota and Curtis Jones had cancelled out earlier strikes from Ethan Pinnock and Vitaly Janelt and looked to have secured Liverpool the win but Brentford came back again to earn a point.
It was Brentford who got the scoring underway first with Pinnock sliding in at the back post off a free kick on 27 minutes to send them in front.
However, it took Liverpool just four minutes to equalise when Jota got on the end of a Jordan Henderson cross which he headed into the goal.
The teams were level going into the second half but Liverpool dominated possession and were rewarded early on when Salah volleyed the ball into the net on 54 minutes to bring his all-time Premier League goal tally to 102.
The assistant referee flagged for offside but VAR overturned the decision and allowed the goal.
Despite seeing little of the ball, Brentford took their chances when they came and Janelt headed them level on 63 minutes from close range.
It was another cross that caught Liverpool out in the final 10 minutes as Wissa chipped the ball over Alisson to level the score.