The Reds got a goal back when Jordan Henderson linked up with Mohamed Salah, who cut the ball back for Roberto Firmino to score. A VAR review was required to confirm Salah was onside and reduce the deficit to one before the half-time break.
Luis Diaz was introduced at the break, and Liverpool didn't take long to restore parity as a result of his play on the left-hand side. The Colombia international looked to isolate defenders, and he soon found Firmino, who beat his man inside the box before finishing clinically past Robert Sanchez.
Buoyed by momentum, Jurgen Klopp's side completed their comeback less than 10 minutes later. Trent Alexander-Arnold's corner wasn't dealt with by Sanchez, and there wasn't much Adam Webster could do as the ball deflected off him and into the back of the net.
Liverpool looked in control after managing to get themselves in front until a cross from the left-flank was missed by Virgil van Dijk in the 83rd minute, finding Trossard, who made no mistake with the finish at the back post.
Alexander-Arnold's free kick required a touch from Sanchez late on to secure a well-earned point for the visitors.
A strong response from the Reds after going 2-0 down saw them swing momentum back into their favour, with much more intensity helping them create chances to win the game. Firmino was clinical when called upon.
Liverpool had to rely on Alisson frequently, with the Brazil international goalkeeper making a number of important saves. The defence seemed to lose concentration in spells, and they could have easily conceded more than the three goals on another day.
Manager rating (out of 10; 10 = best)
Jurgen Klopp, 7 - It would be harsh to blame Jurgen Klopp for Liverpool's poor start, with avoidable errors leading to both goals conceded. The introduction of Diaz was game-changing, helping the Reds level the scores quickly after the restart.
Player ratings (players introduced after 70 minutes get no rating)
GK Alisson 8 - Brighton could have found themselves 3-0 up within the opening 15 minutes but for the interventions of Alisson, who did his best to keep Liverpool in the game with important saves.
DF Konstantinos Tsimikas 7 - The Greece international was one of Liverpool's brighter players in defence, impressing when going forward while preventing danger from coming down his flank. Replaced by James Milner close to the hour mark.
DF Virgil van Dijk 6 - A vital intervention prevented what could have been a goal after a dangerous cross was fired across the box, but the Liverpool defender must do better with the ball that got past him for Brighton's equaliser.
DF Joel Matip 7 - Looked to bring the ball out from the back when possible and was positive in possession. The 31-year-old also made a number of important clearances across the game.
DF Trent Alexander-Arnold 5 - A poor decision to chest the ball down saw the right-back dispossessed and punished as Trossard doubled Brighton's lead. The Liverpool star did look better in the second-half, but there are moments in the game he will be looking to cut out in the future.
MF Fabinho 5 - Seemed slow to react in the buildup to Brighton's first goal, and could have taken up a better starting position. The 28-year-old's passing could have been better at times, and he looked laboured in moments.
MF Jordan Henderson 8 - The Liverpool captain showed positive aggression from midfield and was the player in the middle of the park who looked most likely to recover possession. His key pass over the top that found Salah led to the Reds pulling a goal back before the break, and he also had a hand in Liverpool's goal by helping begin the counter-attack.
FW Fabio Carvalho 6 - The 20-year-old looked bright when in possession, but the Reds rarely managed to get him on the ball in the right areas. While he was replaced at half-time by Diaz, this was unrelated to his performance.
FW Roberto Firmino 8 - A VAR check was required for Firmino's first goal, but there was no question about the second as he beat his man adeptly in the box before finishing on his left-foot to level the scoring.
FW Mohamed Salah 7 - Salah had Liverpool's best chance of the first half when drawing a strong save from Sanchez, and moments later, it was the star right-winger who timed his run perfectly before finding Firmino to score.
Luis Diaz (Carvalho, 46) 7 - Made an instant impact as he regularly challenged Brighton defenders down the left channel before picking up an assist for the equaliser when finding Firmino.
James Milner (Tsimikas 59) 6 - Stretched the play well, but he could have been tighter to Trossard who completed his hat trick in the 83rd minute.
Harvey Elliott (Henderson, 59) 6 - The England under-21 international was impressive with his aggression in midfield, helping maintain Liverpool's press late into the game.
Diogo Jota (Firmino, 76) N/R - Brought on in place of Firmino for the final stages of the game.
Darwin Nunez (Thiago, 89) N/R - Introduced for Thiago as Klopp looked to find a match-winning goal.