Despite the misty conditions at the Amex, Albion found plenty of clear routes to goal, but they once again failed to take some clear-cut chances.
The hosts were on top for large parts, but it was Fulham who almost created the ultimate smash-and-grab scenario with the last kick of the game.
Graham Potter made just one change to the side that won at Leeds ten days ago, with Yves Bissouma coming into midfield and Dan Burn dropping to the bench. Aaron Connolly and Adam Lallana were back among the substitutes.
There was a good tempo to the game from the start. Tosi Adarabioyo advanced from midfield to drive a shot from distance just over but Albion settled and missed three good chances in the space of four minutes.
Seagulls press early on
Adarabioyo failed to deal with Joel Veltman’s ball down the right and Neal Maupay surged into the box, before squaring it to the unmarked Leandro Trossard but from inside twelve yards goalkeeper Alphonse Areola made a good save with his legs.
Trossard then had another great opportunity moments later when Fulham gave the ball away but the Belgian was again thwarted by Areola. Lewis Dunk then met Pascal Gross’ free kick with a towering header but it was straight at the French stopper.
The Seagulls could and probably should have been two or three goals to the good midway through the first half. Trossard’s low cross only just eluded Maupay at full stretch and every time they pressed forwards they carried a threat.
However, it was still goalless and suddenly Fulham threatened again. Bobby De Cordova-Reid popped up at the back post to see his header flash wide before some pressure from Ruben Loftus-Cheek high up the pitch released Ivan Cavaleiro to run at Adam Webster, but his firmly struck shot whistled wide.
Back came Brighton. When Maupay was fouled on the edge of the D, Gross drilled the free kick a yard wide and after the break the hosts continued to carry the greater threat.
Gross swept Veltman’s cut-back goalwards and it took a deflection away from goal but Fulham looked a lot more organised defensively and got numbers back to protect Areola for the first part of the second period.
But Albion had another golden chance in the 70th minute. Alex Mac Allister’s pass following a quickly-taken free kick found Maupay in space 16 yards out, but frustratingly he failed to keep his shot on target when one on one before Webster headed a corner narrowly wide with 13 minutes to go.
The Seagulls kept coming. Areola somehow denied Maupay with his feet when he seemed certain to convert Veltman’s pass and when Solly March latched onto the loose ball his effort, which was bound for the top corner, was deflected over by Andre-Frank Zambo Anguissa.
But it was Fulham who nearly won it in stoppage time. Joe Bryan crossed in to Loftus-Cheek who steered the ball past Robert Sanchez but only for a last-ditch lunge from Dunk to clear off the line.
Had it gone in, it would have been very harsh on Albion, but a point does neither team any favours in the battle to beat the drop.