West Bromwich Albion kept alive their slender hopes of avoiding Premier League relegation with a 1-0 win against Newcastle, while Southampton beat Bournemouth 2-1 to breathe new life into their fight for survival on Saturday.
Albion would have been relegated to the Championship if they had failed to take maximum points at St James' Park, but Matt Phillips bagged the first half winner to keep them in with a shout for a few more hours at least.
Jake Livermore's pin-point pass sent Phillips racing clear of the Newcastle defence and the winger lashed past Martin Dubravka in the 29th minute.
Despite Phillips' strike, bottom of the table Albion's eight-season stay in the top-flight would still be over if 17th placed Swansea beat Chelsea at the Liberty Stadium later on Saturday.
Dusan Tadic boosted Southampton's bid to beat the drop as his double sealed a crucial success in the south-coast derby at St Mary's.
Mark Hughes' third bottom side took the lead when Serbia winger Tadic finished off a rapid counter-attack from Mario Lemina in the 25th minute.
Josh King equalised for Bournemouth with a close-range finish after Saints failed to clear a corner in first half stoppage-time.
But Southampton restored their advantage in the 54th minute thanks to a gem from Tadic, who embarked on a fine solo run before finishing in clinical fashion.
It was Southampton's first league win in five matches since Hughes replaced the sacked Mauricio Pellegrino last month
Southampton, hoping to extend their six-season stay in the top flight, are one point adrift of safety with three games left.
Jurgen Klopp admitted Liverpool were below their best as they prepared for the Champions League semi-final second leg clash with Roma by settling for a goalless stalemate against Stoke at Anfield.
The Reds head to Rome on Wednesday with a 5-2 advantage from the first leg and do so on the back of a tame encounter they controlled for long periods without over-exerting themselves in search of a winner.
The draw left Liverpool needing a maximum of four points from their remaining two matches to guarantee qualification for the Champions League via a top four finish.
"I saw everything I wanted to see except fluency and fun and joy," Klopp said. "It is hard on a day like this. But no-one was seriously injured so we carry on."
Second bottom Stoke are three points from safety, but boss Paul Lambert said: "I could not have asked for any more. If the lads had played like that from the start of the season, I would not be here and they would be cruising in the league."
Crystal Palace are on course to avoid relegation after thrashing Leicester 5-0 at Selhurst Park.
Roy Hodgson's men went in front when Wilfried Zaha took James McArthur's back-heel and fired into the roof of the net in the 17th minute.
McArthur scored in the 38th minute before Leicester had Marc Albrighton sent off for a professional foul in the 56th minute.
Ruben Loftus-Cheek netted in the 81st minute and Patrick van Aanholt struck three minutes later.
Christian Benteke converted a last minute penalty as Palace moved six points clear of the bottom three.
Everton pushed Huddersfield deeper into the relegation mire as goals from Cenk Tosun and Idrissa Gueye earned a 2-0 win at the John Smith's Stadium.
Tosun put Everton ahead from Theo Walcott's cross in the 39th minute and Gueye netted in the 77th minute to leave Huddersfield just three points clear of the bottom three.
Burnley, in seventh and chasing a Europa League place, were held to a 0-0 draw by Brighton at Turf Moor.