Lewis Dunk rescued a point for Albion in another pulsating 2-2 draw.
The Seagulls followed their first European point, achieved by that same scoreline in Marseille, by adding to their Premier League tally less than 72 hours later in what they had allowed to become adversity.
They earlier saw a Mo Salah double turn the tables after Simon Adingra had put them in charge.
It was a hugely enjoyable contest with full parts played by Igor Julio and Carlos Baleba on their first Premier League starts as Roberto De Zerbi made six changes to his XI from the Velodrome.
And it was one with plenty of twists and turns.
As in France, Albion were behind at the break, but this time it was despite playing perhaps their best football of the season for long periods.
Their passing was crisp, sharp and confident and both Igor and Baleba settled well.
They also showed signs of invention at set-pieces, including the corner from which Joao Pedro saw his point-blank shot deflect wide.
The opener was reward for quick thought and actions of Adingra, who spotted Virgil Van Dijk play a pass into the feet of Alexis Mac Allister.
Albion have seen the Argentinean receive the ball in those areas and circumstances before.
Adingra nicked the ball off him, made ground and then ever so coolly passed it beyond the out-of-position Alisson.
Albion buzzed forward - and Baleba powered down the middle, getting fans from their seats, before shooting narrowly wide.
Liverpool fans behind Alisson’s goal demanded better from their side. So did Jurgen Klopp as build-up play stalled.
The lifeline came after Albion lost the ball in their own half.
There was still plenty for Liverpool to do but they worked it nicely before Salah expertly guided his shot across Bart Verbruggen.
Albion did not deserve to be only on level terms but worse was to follow.
Gross lost possession when he took a short pass from Verbruggen.
Dominik Szoboszlai, who had pinched the ball, was then pulled back by Gross and Salah converted the penalty.
Szoboszlai must have thought he had created another goal early in the second period when his low cross was turned on to the bar by half-time substitute Ryan Gravenberch.
Albion also went close, Alisson saving very well from Adingra, who cut inside and shot.
There was plenty of attacking intent for the hosts.
They called for a penalty when Mitoma’s shot hit Van Dijk’s hand – but it had bounced there off his thigh and the protests on and off the pitch led only to a yellow card for De Zerbi.
But a free-kick gave the hosts their route back to level terms.
March was fouled, whipped in a tempting delivery and Dunk volleyed home as Liverpool players waited for each other to deal with the danger.
Both teams pushed for a winner in a grandstand finish and Joao Pedro swept the best chance over the bar after being found by Adingra.
It was a terrific finale to a fine contest – and, ultimately amid all the talking points and turning points, it was a good point for the Seagulls.
Albion: Verbruggen,; Veltman, Dunk, Igor (van Hecke 63), March; Baleba, Gross; Adingra, Joao Pedro (Fati 89), Mitoma; Ferguson (Welbeck 60). Subs Not Used: Webster, Dahoud, Gilmour, Lallana, Steele, Hinshelwood.
Booked: Baleba.
Goals: Adingra 20, Dunk 78.
Liverpool: Alisson; Alexander-Arnold (Gomez 80), Matip (Konate 73), van Dijk, Robertson; Szoboszlai, Mac Allister, Elliott (Gravenberch 46); Salah, Nunez, Diaz. Subs Not Used: Endo,Adrian,Tsimikas,Chambers,Doak,Quansah.
Booked: Szoboszlai, Gomez.
Goals: Salah 40, 45 pen.
Att: 31,752
Ref: Anthony Taylor (Cheshire).
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