Nathan Redmond's first-half double sent Southampton on their way towards safety as they wrapped up a 3-1 win over Wolves.
Willy Boly's header after 28 minutes had temporarily hauled the visitors back on level terms but Redmond put Saints back in front two minutes later, and Republic of Ireland striker Shane Long secured the points after 71.
Cardiff were plunged deeper into relegation trouble after Chris Wood scored twice to give Burnley a controversial 2-0 win at Turf Moor.
Wood headed home from a Dwight McNeil corner to cap a dominant first-half performance but Neil Warnock's side were seething early in the second half after being denied a penalty.
Referee Mike Dean originally penalised Burnley defender Ben Mee for handball but then reversed his decision, much to the evident displeasure of the visiting players and manager.
Burnley made the most of their reprieve as they continued to dominate the game and Wood nodded home his second from point-blank range in the last minute.
Cardiff's survival hopes could now rest on their midweek trip to ailing Brighton who were hammered 5-0 at home by Bournemouth.
Dan Gosling gave the visitors the half-time advantage and Ryan Fraser added a second before Brighton's Anthony Knockaert was sent off for a dreadful lunge on Adam Smith.
Eddie Howe's side wrapped up an emphatic victory with further goals from David Brooks, Callum Wilson and Junior Stanislas.
Already-relegated Fulham produced one of their best performances of the season as they beat Everton 2-0 at Craven Cottage.
Tom Cairney struck his first Premier League goal shortly after the re-start and Ryan Babel clipped his side's second over Jordan Pickford to secure Scott Parker's first win as caretaker boss.
In the early kick-off, Lucas Moura struck a hat-trick as Tottenham continued to revel in their new home comforts, cruising to a 4-0 win over already-relegated Huddersfield.