Palace's victory lifts Roy Hodson's side up to 16th in the table
On another important day at the bottom of the Premier League, Crystal Palace were the big winners as they beat fellow strugglers Huddersfield to climb out of the relegation zone.
Luka Milivojevic's second-half penalty sealed a vital 2-0 win for Palace. Their first victory in eight matches lifts them up to 16th in the table, two points clear of the bottom three.
Huddersfield remain one point above Roy Hodgson's side in 15th, with Southampton slipping down into danger and 18th place. Saints play at Wigan in the FA Cup on Sunday.
There was also more suffering for West Brom. They ended up losing 2-1 at Bournemouth on the south coast, having gone ahead through Jay Rodrguez's strike just after the break.
Jordon Ibe levelled the scores with 13 minutes to play, and Junior Stanislas' free-kick stole all three points for the Cherries in the 89th minute.
Alan Pardew's side remain bottom of the table, now 10 points short of safety with just seven matches left.
Meanwhile, fellow strugglers Stoke stay 19th after a 2-1 defeat at home to Everton. Charlie Adam was sent off for a lunging challenge on Wayne Rooney in the first half of a match played in wild wintry conditions.
There was wind, snow and brilliant sunshine as a record attendance of 30,022 at the Bet365 Stadium saw the Potters lose out to Cenk Tosun's second-half double.
Paul Lambert's side are three points away from 17th place as they bid to extend their 10-year stay in the top flight.
Bournemouth 2-1 West BromHuddersfield 0-2 Crystal PalaceStoke 1-2 Everton Adam was shown a straight red card for this challenge on ex-England captain Rooney
Still to come, Liverpool welcome Watford in the 17:30 GMT kick-off. A win for Jurgen Klopp's side would take them up into third and above Tottenham, who were playing in the FA Cup this weekend.
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FA Cup: Swansea 0-3 Tottenham highlights
Earlier on Saturday, Spurs booked their place in the FA Cup semi-finals with a dominant 3-0 victory at Swansea.
Manchester United play Brighton at home in their quarter-final in a 19:45 kick-off.
And on Sunday there are two last-eight ties live on BBC One. League One Wigan play Southampton at 13:30, before Leicester host Chelsea at 16:30.
Swansea 0-3 TottenhamManchester United v BrightonWigan v SouthamptonLeicester v Chelsea
Source: bbc.com