A first half header from Matt Smith saw Blackpool lose again.
Smith’s eighth-minute header was enough to secure the win, which put Fulham nine points clear of third-bottom Millwall. The Lions have three games left, but the Cottagers have a superior goal difference.
Blackpool are now without a win in their last 16 games and still require one point to equal the lowest tally ever posted since the second tier became 24 teams in 1988.
The hosts went close to making the breakthrough after just four minutes when Gary Madine slipped Henry Cameron clean through on goal, but the midfielder’s effort from 18 yards came back off the post.
Less than a minute later, Cameron was in behind the Fulham defence again but was denied from similar range by the fingertips of Marcus Bettinelli.
But, in the manner typical of Blackpool’s season, it was Fulham who opened the scoring in the eighth minute when Sean Kavanagh’s cross from the left was nodded into the bottom-left corner by Smith from 12 yards.
Smith had the chance to double the visitors’ lead in the 14th minute, but lashed over from 12 yards after gathering Ross McCormack’s right-wing cross.
Fulham continued to pressurise the leakiest defence in the Football League and big striker Smith was almost on target again in the 17th minute, but sent his header wide when six yards out from a corner.
Blackpool could have drawn level after 22 minutes when Jamie O’Hara’s corner evaded Bettinelli, but it was nodded wide by the flying Jose Cubero.
Fulham were dealt an injury blow early in the second half when influential striker Smith was forced off.
O’Hara then went close with a dipping left-footed strike from 18 yards in the 52nd minute, but it clipped the top of the net on its way over.
Two minutes later it was Fulham threatening to find the net, but unmarked substitute Cauley Woodrow headed McCormack’s free-kick high over the bar from 12 yards.
And the visitors looked certain to score in the 57th minute but Kavanagh’s low cross from the left somehow evaded Woodrow who was just three yards out with the goal gaping.
Fulham threatened down the left side again after 69 minutes but James Husband’s low cross was behind McCormack with the striker waiting, unmarked, six yards out.
Blackpool substitute Nathan Delfouneso went within inches of equalising after 76 minutes when he beat Bettinelli to the ball, but his effort across goal was hooked off the line by Ashley Richards.
The Cottagers looked to secure the win on the counter-attack in the 80th minute, but McCormack’s strike from 20 yards was straight at Elliot Parish.
Madine almost grabbed a late equaliser but his dipping strike from 20 yards was superbly tipped around the post by Bettinelli.