Roberto de Zerbi's debut as a coach was marked by a hugely entertaining and battling draw against the Reds.
After making a slow start, the Seagulls raced into a two-goal lead with the Reds.
Trossard got the first after just four minutes when he thumped into the bottom corner from Danny Welbeck's pass before adding a second 13 minutes later.
Roberto Firmino's goal was given by the video assistant referee after initially being ruled out for an obstruction.
Firmino scored from close range nine minutes after the break when he wrongfooted his marker and LuisDiaz found him.
There was a sense of inevitability as a hungryLiverpool continued to come forward and they duly got a third when AdamWebster turned into his own net under pressure from Firmino
The match ball and a point were secured by Trossard as he scored at the back post.
With one game in hand, the ninth place team is 11 points behind the leaders but still in the running.
This was a game that highlighted the best and worst of the current team.
On the other hand, the fightback was reminiscent of the old days of the Reds where, after a terrible first 25 minutes, there was a growing sense that they'd get themselves ahead at some point.
It was a bad start that cost them the three points.
The Reds have conceded the first goal in five of their seven games this season and it's a challenge for the manager to figure out how to get them back on track.
They need to rediscover their focus before the title race gets away from them because of the determination and character that took them to within a point of City last season.
The distance and rail disruption did not deter fans from travelling to witness what datememe datememe looks like.
Fans of the Seagulls have been promised entertaining but risky football from their new manager, who replaced Graham Potter.
They could have won 6-3, but also could have lost by the same score.
They were energetic and direct in the first 25 minutes, but tired after that, but they still showed a lot of spirit in the closing stages.
Life after Potter will be an exciting one under De Zerbi, despite the fact that it is still very early.