Brighton started the game strongly and took the lead through Evan Ferguson's neat finish. However, Palhinha's superb strike earned a point for Fulham.
Brighton's winless streak extended to three games as they failed to capitalize on their scoring opportunities.
Roberto De Zerbi's team showed no signs of tiredness after their 2-0 Europa League win over Ajax on Thursday and almost took an early lead.
Fulham goalkeeper Bernd Leno kept out Carlos Baleba’s shot from range in the seventh minute and saved Simon Adingra’s effort inside the six-yard box moments later to keep it 0-0.
Baleba was pulling the strings for Brighton as his vision and inch-perfect passes picked out the pacey Adingra, who enjoyed runs into space.
The hosts got the goal they deserved after 26 minutes.
Igor Julio drove the Seagulls up the pitch and when Ferguson retrieved the ball outside the box he showed excellent composure to slide the ball past Leno with his left foot into the bottom corner.
The goal highlighted a gulf in quality between the two sides and the lethargic Cottagers were fortunate not to concede again immediately after the kick-off when their defence was caught napping by Adingra.
A rain-soaked Marco Silva cut a frustrated figure and his pleas to his Fulham players were left unanswered as Willian’s wasteful free-kick put an end to the first spell of meaningful possession the visitors had enjoyed in the Brighton half since the opening minutes.
Left-back Antonee Robinson was struggling to cope with Adingra and the American then gifted Ferguson a back pass, but the Seagulls’ goalscorer failed to double his tally when he was denied by Leno after 40 minutes.
Brighton started the second half quickly and Lewis Dunk was unfortunate not to score in the 49th minute. The skipper lined up a set-piece and his side-footed effort dipped onto Leno’s crossbar.
Fulham made Brighton pay for their missed chances as they made it 1-1 in the 65th minute through Palhinha.
The visitors threw men forward in numbers and the Portugal international got the ball out of his feet on the edge of the box and blasted an effort past Jason Steele.
The goal swung the momentum in the Londoners’ favour and substitute Rodrigo Muniz nearly punished Brighton from the restart through an audacious back heel that was kept out by Steele.
Both teams had opportunities to win it with Robinson clearing an effort off the line before Harry Wilson came close to grabbing a winner at the other end.
