Following an even opening 20 minutes with few real chances, Michael Kayode came close to delivering the breakthrough for the home side, as a block from Jeremy Jacquet carried his effort narrowly past the post.
Liverpool then broke from the resulting corner, and Bradley Barcola should really have added to his midweek hat-trick against LASK Linz, but he dragged his effort wide after racing through one-on-one with Caoimhin Kelleher.
Igor Thiago almost received a similarly clear-cut opening of his own, but he was denied by another vital intervention from the impressive Jacquet.
The Bees began to grow into the ascendancy, but Liverpool thought they had a spot-kick when Dango Ouattara went flying in on Alexis Mac Allister, only for VAR to correctly inform the referee that it was in fact a perfectly-timed challenge.
The visitors could have no complaints when Keane Lewis-Potter broke the deadlock in the 44th minute, stretching to guide a lovely Thiago cross beyond Alisson.
But in a moment of madness in stoppage time before the break, Yehor Yarmolyuk threw his head at Jacquet as the two wrestled before a corner, earning himself a completely needless red card.
Thiago nearly made things even more complicated for Keith Andrews after the break, escaping with a yellow after seemingly throwing an elbow at Jacquet just 12 seconds into the second half.
With the disadvantage remaining at just one player, Brentford were able to maintain a compact defensive unit, while posing a continued threat of their own on the counter.
Nevertheless, Alexis Mac Allister almost managed to make something happen, skipping past a couple of challenges before forcing a good save from Kelleher.
Eventually, Victor Munoz was the one to find the equaliser, chopping inside smartly and guiding the ball into the corner to break the stubborn resistance.
It was one-way traffic after the goal, and Alexander Isak eventually made it tell, controlling the ball under heavy pressure and guiding it coolly past the goalkeeper to put the Reds in front.
The Bees were then forced to come forward, and Thiago had a great chance to level things up again, but he couldn’t make convincing contact from six yards out.
The crossbar denied Barcola from settling the contest, but Andoni Iraola’s side were able to see out the victory.
This was helped by a second red card in stoppage time for Vitaly Janelt, whose trip stopped a promising Reds counter, having already been booked previously for dissent.
The win marked the Spaniard’s first league success against Brentford in eight attempts (W1, D2, L5) and ends Brentford’s unbeaten start to the league campaign.
Liverpool have also leapfrogged their opponents in the table, with the Bees having started this fixture on top for the first time since 1938.
Flashscore Man of the Match: Alexis Mac Allister (Liverpool)