Though the Seagulls dominated from kick off, they couldn't secure their place in the fourth round of the Carabao cup.
But Brighton fans were grinning as they watched their team - who are going from strength to strength in the Premier League - play at Stamford Bridge in the third round of the cup.
Albion were resilient in their pursuit of a goal but were unable to convert any of their chances on the night.
- READ MORE: Chance missed and De Zerbi knows it
Nicolas Jackson's winning strike - which sealed a home tie against Blackburn at the end of next month - came in the 50th minute.
That goal was the first Chelsea had scored in four matches.
Solly March had the chance to get Brighton level late in the second half when he was left unmarked, but his header was straight at former Seagulls keeper Robert Sanchez.
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