The Belgian forward is the first opposition player to net a top-flight treble at Anfield since Andriy Arshavin did so for Arsenal in a stunning 4-4 tie back in 2009.
He is only the third to do so in the Premier League era, after Arshavin and Peter Ndlovu, who also achieved the feat for Coventry during the 1994/95 campaign.
Liverpool, playing their first league match for 28 days following the international break and postponements that followed the death of Queen Elizabeth II, looked set for another hugely disappointing afternoon on Merseyside when Trossard struck twice inside the opening 20 minutes to give new Seagulls boss De Zerbi the perfect start after succeeding Graham Potter.
The 27-year-old arrowed two shots beyond Alisson Becker and into the far corner, the first of which came after a fine flick from Danny Welbeck and the second teed up by an exquisite touch from Solly March.
Liverpool could easily have been three or four goals behind after a truly sluggish opening, but Roberto Firmino’s effort 10 minutes before half-time was eventually given after a long VAR check with Mohamed Salah initially flagged for offside after squaring Jordan Henderson’s lofted pass to the Brazilian.
Liverpool, to their credit, then stepped up a gear after the interval, with Firmino firing home his second after quick feet to bamboozle Lewis Dunk and level the score after Luis Diaz’s half-time introduction had given Jurgen Klopp’s men a clear spark.
They completed a terrific turnaround through an own goal, with Trent Alexander-Arnold’s corner completely missed by Brighton goalkeeper Robert Sanchez and just evading the head of Diaz at the front post before bouncing in off the arm of the unlucky Adam Webster for 3-2.
But there was still time for Trossard to silence the home crowd again one last time, confidently sweeping home from 12 yards out with only seven minutes to go after substitute Kaoru Mitoma’s cross went straight through the legs of Virgil van Dijk.
Alexander-Arnold thought he had snatched victory for Liverpool in stoppage time, only for Sanchez to make a flying save to repel his free-kick in the dying moments.
Yet more dropped points leave Liverpool – who have won only two of their first seven league games this season – sitting ninth and a full 11 points off the title pace after Arsenal’s impressive north London derby win over Tottenham earlier in the day.
Brighton stay fourth and seven points off the Gunners after a memorable start to the De Zerbi era.