Lewis Dunk's last-minute goal-line clearance denied Fulham the chance to move within two points of safety as they were held to a 0-0 draw at Brighton
The hosts had the best of the chances at the Amex Stadium on the balance of play, with Leandro Trossard forcing a smart save from Alphonse Areola before half-time when he should have scored
Neal Maupay missed the target altogether with another presentable opportunity after the break as Brighton's search for a first home win since June 20 last year continued
But it was Fulham who almost snatched victory in second-half injury time, when Chelsea loanee Ruben Loftus-Cheek's goalbound shot was cleared off the line by Dunk with Robert Sanchez beaten
The draw keeps Brighton five points clear of third-bottom Fulham, although Scott Parker's men have a game in hand on all of the sides around them
All the signs pointed towards a low-scoring game as two of the Premier League's most out-of-form teams went head to head, with one win in 17 games between them, but there was plenty of energy in a high-tempo start at the Amex, where Fulham pressed high from the off
That pressure did not transfer into chances for the visitors, though, and when Brighton did find a way through, they should have opened the scoring as Trossard fired Maupay's cut-back straight at Areola
He was presented another opportunity when a second chance in quick succession was blocked by Stefan Johansen, before Ivan Cavaleiro selfishly shot wide from a quick break with Fulham still searching for a first shot on target
It would finally arrive 11 minutes into the second period when Ben White's block on Cavaleiro's effort took it safely through to Sanchez, but Brighton continued to make the better chances, and a quickly taken free-kick caught the visitors on the hop and found Maupay in space, but he blazed well over when well-placed
Maupay finally found the target but fired at Areola from Joel Veltman's square ball with time running out, before Fulham finally found their shooting boots in added time
Loftus-Cheek, the visitors' dangerman after half-time, looked to turn a low cross back inside the far corner but with Sanchez beaten, Dunk cleared off the line to deny Fulham a first win in nine and keep them five points from safety
Brighton manager "I think they had one chance in the first half on the break and then the chance at the end for them
"But apart from that, I thought we were the ones pushing in the game
"So, it was positive in terms of the performance, positive in terms of the attitude and the character and the personality of the players, but disappointed not to get the three points
"Fulham boss "We came here to win, we are happy with a clean sheet and a point and we move on
"We defended well, weathered the storm from their set-plays and the keeper has dominated his box well and made some big saves
"This team three or four months ago needed to score three or four goals to win a game
"Starting with the statistics, Dunk won more than 70 per cent of his duels to keep a lively Fulham attack at bay, and had two shots on target, both headers from set-pieces which Areola dealt with
But he also provided the most important moment of the match - without him, Fulham would have left the Amex with three points but his instinctive goal-line cover late on was what he does best, reading the situation and keeping his side's clean sheet intact
Brighton host Tottenham as part of  live on  from 7pm; kick-off at 7
15pm
Fulham have another relegation six-pointer in the shape of West Brom at The Hawthorns on Saturday; kick-off at 3pm
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