A penalty from Wilfried Zaha seemed likely to be enough to decide the match in the London side's favour, but Albion hit back in the 95th minute when Neal Maupay converted following a free kick.
It means that Brighton remain sixth as just one point differentiates the leading six teams.
The Gunners blitzed their rivals in the first half as goals from Emile Smith-Rowe, Pierre-Emerick Aubameyang and Bukayo Saka earned them a 3-0 lead at the break.
A late consolation from Son-Heung Min meant little for the away side.
Spurs, meanwhile, have now lost three on the bounce and the pressure on manager Nuno Espirito Santo is increasing with many fans very unhappy with the new boss.
In what was arguably the best game of the season so far in the English top flight, the Bees twice fought back from behind to make it 3-3 with 10 minutes to go.
Ethan Pinnock opened the scoring but goals either side of the break from Diogo Jota and Mohamed Salah made it 2-1 Liverpool before the hour.
Vitaly Janelt then equalised before Curtis Jones thrashed a strike home to make it 3-2 to Jurgen Klopp's men.
Substitute Yoane Wissa would score with a lovely dink from close range in the 88th minute, however.
In the early Saturday kickoff, Man City secured a massive result away at Stamford Bridge.
Gabriel Jesus scored the only goal of the game as Pep Guardiola's side narrowly emerged victorious 1-0.
At the same time, Man Utd took on Aston Villa at Old Trafford and Ole Gunnar Solskjaer's week went from bad to worse as the Red Devils followed up their League Cup exit with a 1-0 loss at home in the Premier League.
Bruno Fernandes had the chance to equalise late on from the penalty spot, but blazed his attempt over.
West Ham secured a late win away at Leeds, too, thanks to a goal from Michael Antonio.
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