Ethan Pinnock put the Bees in front on 27 minutes when he tapped in at the back post following a free-kick routine from the hosts, but Diogo Jota levelled soon after with a close-range header from a Jordan Henderson cross.
Salah’s 100th Premier League goal for the Reds gave them the lead in the early stages of the second half, making him the quickest player in the club’s history to achieve the feat.
Vitaly Janelt then drew Brentford level with a header inside the box after the ball had come back off the crossbar, before Curtis Jones fired Liverpool back ahead with a stunning blast from distance.
Yoane Wissa would ensure the spoils were shared, however, by converting from close range in the closing stages of the contest.
Team news…
Liverpool made 10 changes from the midweek Carabao Cup victory over Norwich City, with only Jones retaining a place in the starting XI. Elsewhere, Joel Matip returned after being rested while Roberto Firmino was back on the bench after recovering from injury.
Liverpool: Alisson, Alexander-Arnold, Matip, Van Dijk, Robertson, Fabinho, Henderson, Jones, Mane, Salah, Jota.
Subs: Kelleher, Konate, Milner, Firmino, Gomez, Oxlade-Chamberlain, Minamino, Tsimikas, Origi.
First half…
In their first trip to Brentford since 1983, Liverpool kicked off knowing they could establish a clear lead at the top of the fledgling Premier League table following Chelsea’s home defeat by Manchester City earlier on Saturday.
The Reds set about quickly asserting themselves, too, and they were a fraction away from taking the lead in the seventh minute when tenacious work from Jones in midfield reclaimed possession for the visitors and resulted in Jota sliding a pass through for Salah to race clear.
He prodded the ball beyond the advancing David Raya, but Kristoffer Ajer was able to get back to prevent it from crossing the line with a sliding recovery.
But Brentford demonstrated why they’ve made such a promising start to life in the top flight in response, with Ivan Toney glancing a header well wide before Frank Onyeka caused more concern when he scooped a shot over the bar from close range.
The Bees went closer still on 11 minutes, but Matip was on hand to clear an effort from Bryan Mbeumo on the line after the initial shot had beaten Alisson Becker.
However, the home side would open the scoring with 27 on the clock. A set-piece routine resulted in Sergi Canos’ cross being touched across goal by Toney, allowing Pinnock to tap in at the back post from yards out.
Their advantage was a short-lived one, though, as Liverpool mustered an instant riposte.
Salah found Henderson in space on the right and the captain hung a cross into the centre of the area, where Jota expertly guided the ball into the corner with his head to level up the score.
The Portugal forward was denied a second soon after as Raya blocked his seemingly goal-bound effort with his head after Jones’ low drive had deflected against the base of the post.
Second half…
The lively nature of the meeting didn’t diminish with the interval – and Liverpool threatened four minutes after the restart when Raya needed to claw a bouncing ball away at the foot of the post after Henderson’s glancing header had deflected off Jota’s knee and diverted goalwards.
Nevertheless, the Reds were in front shortly after – and it was a landmark goal for Salah, who sublimely swept in a first-time finish from Fabinho’s pass over the top.
A VAR check delayed the celebrations, but it was to be Salah’s 100th in the Premier League for the club – and in netting, he became the quickest player in Liverpool history to a league century.
It signalled the start of the teams trading goals in a period that saw the game swing one way and then the other in electrifying fashion.
First, Brentford levelled when Pontus Jansson crashed an effort against the crossbar on the turn before Janelt looped the rebound over the line with a header.
Then, Jürgen Klopp’s team regained the lead in spectacular fashion as Jones rocketed a drive in at the near post from 25 yards, with the ball taking a touch off Ajer before finding the net.
But Brentford would restore parity yet again through substitute Wissa, who clipped a loose ball over Alisson from six yards out after a scramble in the area.
The home side needed a touch from Ajer to prevent Firmino tapping in during stoppage time as Thomas Frank’s men claimed a share of the points.