Jurgen Klopp's men were starring down the barrel of a first league defeat in front of fans at Anfield since 2017 when the Belgian scored twice inside the first 17 minutes.
Liverpool have won only won two of their first seven league games of the season to already fall 11 points behind leaders Arsenal.
The Reds looked to have turned the game around when Roberto Firmino struck twice either side of half-time before Adam Webster's own goal put the home side in front.
But in Roberto De Zerbi's first game as Brighton boss, the Seagulls got the reward their performance deserved when Trossard fired in at the back post seven minutes from time.
A point leaves Liverpool down in ninth, while Brighton remain in fourth.
De Zerbi's debut lived up to the hype as the Italian's brand of intricate passing out from the back cut Liverpool to shreds in the early stages.
Klopp spoke out at length in defence of Trent Alexander-Arnold after he was overlooked by England manager Gareth Southgate during the international break.
But critics of Alexander-Arnold's defending were given more ammunition after just four minutes when he was turned by Trossard and the Belgian fired into the far corner.
A nightmare opening 20 minutes for the hosts could have been much worse but for two big saves from Alisson Becker.
Danny Welbeck placed his header from close range too close to the Brazilian, who then produced a brilliant stop as he flew off his line to deny Trossard.
However, Liverpool were not so lucky when they passed up a third big chance after the opener as Brighton again worked an opening down the side of Alexander-Arnold and Trossard's strike had too much power for Alisson.
#photo1
Klopp summoned Virgil van Dijk to the touchline after the second goal in a bid to restore some order and the Reds did get a foothold before the break.
Firmino's fourth goal of the season was initially ruled out for offside as he dinked into an unguarded net after Mohamed Salah knocked the ball past Robert Sanchez.
A VAR review came to Liverpool's rescue, though, to halve the arrears.
Klopp had surprisingly left Luis Diaz, Diogo Jota and Darwin Nunez on the bench from the start, but Diaz replaced Fabio Carvalho at the start of the second half.
The Colombian made a quick impact as he charged at the Brighton defence and laid the ball across for Firmino, who cut inside Lewis Dunk and coolly found the far corner.
Firmino's future is uncertain with the Brazilian's contract set to expire at the end of the season.
But his renaissance in front of goal should have resulted in a hat-trick as he headed straight at Sanchez with the chance to complete the comeback.
Welbeck should have restored Brighton's lead when he failed to connect with a low cross from close range.
Moments later, the Seagulls were behind thanks to a calamitous goalkeeping error from Sanchez.
Not for the first time this season, the Spanish international flapped at a corner and punched the ball into his own net off the unfortunate Webster.
True to De Zerbi's reputation as an attack-minded coach, Brighton never stopped piling men forward and finally took one of their chances when Trossard turned home Kaoru Mitoma's cross.
