Bolton Wanderers secured a priceless three points in their bid to escape relegation on Saturday, winning 1-0 at Middlesbrough.
Gavin McCann struck after the break at the Riverside to take Wanderers out of the relegation zone, above Birmingham City and Reading, who had earlier lost 2-0 at Arsenal.
Reading could find themselves in the relegation zone on Sunday should Birmingham beat Aston Villa.
While Bolton earned a second consecutive 1-0 victory to claw themselves towards safety, things were looking grim for Fulham who lost 2-0 at home to a below-strength Liverpool.
Jermaine Pennant and Peter Crouch, both of whom are unlikely to start in Liverpool's Champions League semi-final, first leg against Chelsea next week, were on target to leave Fulham five points from the safety zone with three games to play.
Liverpool are now eight points clear of fifth-placed Everton and on target for a Champions League qualifying place next season.
Meanwhile, leaders Manchester United were held to a 1-1 draw by Blackburn Rovers at Ewood Park in a late kick-off.
Argentine Carlos Tevez headed in an equaliser in the 89th minute to cancel out Roque Santa Cruz's 23rd minute goal which had put the home team ahead.
Sir Alex Ferguson's team is now just three points ahead of Chelsea with three games left in the season.
Wigan Athletic edged a point nearer survival with a 1-1 draw at home to mid-table Tottenham Hotspur while relegated Derby County went down 2-1 at West Ham United.
With just one win and 11 points Derby are on course to become the worst team in Premier League history.
At the top of the table, Manchester United can go five points clear of Chelsea with three games left if they win at Blackburn Rovers in the day's late kickoff.
Bolton manager Gary Megson said his side had been level at halftime more "by luck than judgement" but was relieved they had improved to win for just the second time away this season.
"It was a big boost to get three points away from home," Megson told Sky Sports. "We were rocking in the first half but were much better after the break."
McCann struck the winner after 60 minutes, volleying in after Middlesbrough keeper Ross Turnball had saved Gary Cahill's close-range header.
