Mo Salah had earlier scored his 100th Premier League goal for the Reds but Yoane Wissa’s 82nd minute equaliser saw the Bees continue their terrific start to life in the top flight.
Both sides had efforts cleared off the line in a lively opening before Ethan Pinnock gave Brentford the lead, stabbing the ball home at the back post after a clever free kick routine caught the Liverpool defence flat-footed in the 27th minute.
That lead was short-lived as Diogo Jota headed home Jordan Henderson’s cross to put the Reds level four minutes later, and Salah put his side in front in the 54th with his 100th goal in 151 league appearances for Liverpool.
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 Wissa eight minutes from time.
The win 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, a result which sent the Reds top on goal difference even before they’d kicked a ball. Brentford move up to ninth on nine points.
Additional reporting by Reuters.