Spurs' lead over Arsenal in the battle for fourth place in the Premier League remains three points, but the Gunners now have two games in hand.
Antonio Conte's men had won four consecutive games, starting with a 2-0 win at Brighton last month, to turnaround the Italian's rollercoaster first season in charge.
However, the prolific Harry Kane and Son Heung-min were kept very quiet as the home side struggled to create any clear-cut chances.
Brighton did Tottenham a big favour by ending a seven-game winless run last weekend at Arsenal.
With confidence restored, the Seagulls looked more like their old selves under Graham Potter as they controlled the game and completed a north London double thanks to Trossard's composed finish in the final minute.
Kane's most significant contribution came inside his own six-yard box as he blocked Joel Veltman's effort with the best chance of a first-half only enlivened by controversial refereeing calls.
Both sides were lucky to still have 11 men on the field by the break as Tottenham's Dejan Kulusevski escaped with just a yellow card for a swinging elbow on Marc Cucurella.
Cucurella then took revenge with a stamp on Kulusevski's ankle, while Enock Mwepu twice avoided a potential second yellow card.
Tottenham only marginally improved in the second period as Trossard blocked Son's effort from close range before Rodrigo Bentancur flashed a follow-up shot wide.
Brighton continued to pose the greater threat with Hugo Lloris tested by a header from Lewis Dunk.
Trossard produced the moment of quality the game had needed for 90 minutes when he sold Eric Dier a dummy to create the space for a prodded finish past Lloris.
Spurs' best chance of the match came just seconds later when Kane flicked a header into the path of Steven Bergwijn, but the Dutchman scuffed well wide to sum up their day.
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