The Bees refused to give up, levelling in the 63rd minute when defender Pontus Jansson swivelled in the box and hit the crossbar before Vitaly Janelt reacted quickest to head home the rebound.
Curtis Jones put Liverpool back in front four minutes later, cutting in from the left and unleashing a rocket that took a slight deflection before flying into the net, but Brentford snatched a dramatic equaliser through substitute Yoane Wissa in the 82nd minute.
The draw sees Liverpool climb to 14 points after six games, one ahead of Manchester City, who beat Chelsea 1-0 at Stamford Bridge earlier in the day. Brentford move up to ninth on nine points.
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