Leicester City equalled the 24-year-old record for the biggest ever Premier League victory as 10-man Southampton were dismantled at a rainswept St Mary's.
The victory sees Brendan Rodgers' side climb into second place, leapfrogging Manchester City and moving five points behind leaders Liverpool.
Southampton manager Ralph Hasenhuttl said his side knew it was "time to show up" after they carved out a point against Wolves.
"You could feel it in the dressing room. Everyone knew it was time to show up," said Hasenhuttl.
"We started well but to be honest we are far away from our best, and against the best opponents you only have the chance to take something if you play your best.
"We were too slow in our minds, too slow on the ball.
Maurcio Pochettino says he will shoulder the "blame" for Hugo Lloris' howler in 10-man Tottenham's 2-1 Premier League win over Southampton.
The France goalkeeper - and 2018 World Cup winner - was inexplicably dispossessed inside his own six-yard area by Danny Ings for Saints' equaliser following a back pass.
Bournemouth survived a second-half fightback to secure a first ever victory at Southampton and move into third place in the Premier League before the weekend's games.
Bournemouth manager Eddie Howe says they "need to keep grounded" after moving up to third in the Premier League with a first win at Southampton.
Sheffield United boss Chris Wilder says his side "have to wise up quickly" after they were beaten by Southampton in a tight game at Bramall Lane.
The Blades have now won just one of their opening five games on their Premier League return.
Jannik Vestergaard's towering header gave 10-man Southampton a point after another moment of magic from Manchester United new boy Daniel James looked to have put them on course for victory at St Mary's.
Brighton manager Graham Potter said he "can't defend" Florin Andone's challenge which resulted in the Romanian's dismissal in the Seagulls' 2-0 defeat to Southampton.
"It didn't look like a great tackle," Potter told Match of the Day.
Nathan Redmond's wonder-goal was not enough for Southampton as they were held to a 1-1 draw by Huddersfield on the final day of the Premier League season
Southampton vs Huddersfield Town Highlights
Start date: 12.
West Ham United vs Southampton Highlights
Start date: 04. May 2019, 15:00
Location: London Venue: London Stadium
Referee: Stuart Attwell, England
Manager Manuel Pellegrini hailed West Ham's "special season" as their bid for a top-10 finish was enhanced with a comfortable victory over Southampton.