Saints' keeper Angus Gunn saved Theo Walcott's penalty and defender Cedric slotted his effort past Maarten Stekelenburg to put the visitors into the last-16 where they will play away at Leicester City.
Chelsea stay a point clear of Arsene Wenger's unbeaten team with 36 points.
Monday's resumption was also a chance for those jostling at the top of the table to lay down a marker and for the strugglers to enjoy a fresh start.
Jamie Vardy wrote a new chapter in his fairytale rise from the wilderness of non-League football to playing for England, when he became the first player to score in 11 consecutive Premier League matches on Saturday.
Jack Wilshere and Harry Kane have been recalled to the England squad for Friday's World Cup qualifier against Scotland and a friendly against Spain, the FA announced on Sunday.
Here are the talking points from the weekend's action in the Premier League
Images from the English Premier League matches played on Saturday
Chelsea must improve their defensive solidity if they are to challenge for silverware this season, winger Eden Hazard has said. Despite coach Antonio Conte's reputation of building teams around a solid defensive unit, Chelsea have conceded nine league goals this season, including three against Arsenal on Saturday, the first of which came from an error by Gary Cahill. The London club have kept just one clean sheet in six league games this campaign.
English football giants Manchester United confirmed being hit by a cyber attack in a 'sophisticated' operation.
Former Cup winners Coventry, now plying their trade in the bottom division of the Football League, revived memories of happier times as Jordan Willis and Jack Grimmer scored the goals in a 2-1 victory at the Ricoh Arena.
IMAGES from the English Premier League match played between Arsenal and Chelsea at Emirates Stadium in London on Sunday.
The dynasty will only be built on European success, though, and after the quarter-final exit to Liverpool, Manchester City's owners, who want a gilded continental powerhouse to match United's global lustre, will demand it and back those demands with huge funding.
Manchester City squandered a gilt-edged opportunity to close the gap on Premier League leaders Chelsea when they let slip a two-goal lead to draw 2-2 at home to struggling Burnley on Sunday.
Chelsea came from behind to secure a 3-1 win at Manchester City and forge further clear at the top of the Premier League as a dramatic top-of-the-table clash ended in a mass brawl and two City players being sent off on Saturday.
Barcelona were held 1-1 at home by Napoli in the first leg of their Europa League knockout stage playoff
Spanish champions Barcelona have exercised the buy-back clause to re-sign midfielder Denis Suarez from Villarreal, the Catalan club announced on Monday.
Manchester City emerged from a trough of despair to beat Tottenham Hotspur 3-1 and move to within three points of the Premier League title at Wembley on Saturday.
The striker smashed in an 86th-minute winner to give Leeds United a dramatic 3-2 home victory over fellow strugglers Leicester City
Romelu Lukaku scored for Chelsea in a 5-1 FA Cup third-round victory
Manchester United humbled Manchester City 4-2 in the continent's big derby of the weekend.
Under-fire Manchester United boss Jose Mourinho has been priced odds-on to be the first Premier League manager to leave his job this season.
COVID-19 cases in the visiting teams have forced the postponement of the Liverpool v Leeds United and Wolverhampton Wanderers v Watford games scheduled for Boxing Day, the Premier League announced on Thursday.
Granit Xhaka hammered two goals in what is expected to be his last game as Arsenal clinched a 5-o win over Wolves.
Here's a glimpse of all that happened around the world last week.
England striker Daniel Sturridge celebrated his return after a five-month injury layoff when he came off the bench to score as Liverpool beat West Ham United 2-0 in the Premier League on Saturday.
Check out the top footballers of the weekend.
Leicester City's Kelechi Iheanacho scored two poacher's goals as they beat Manchester United 3-1 in their FA Cup quarter-final on Sunday to set up a last-four clash against Southampton.
Schar's goal for Newcastle United in the 1-1 draw with Watford should have been chalked off
Manchester City are top on goal difference, with Chelsea second and Liverpool dropping to third, two points ahead of Arsenal, who routed Fulham 5-1.
A summary of Saturday's action in the Premier League.
IMAGES from the English Premier League matches played on Wednesday
Tottenham Hotspur's tenacious chase of leaders Chelsea continued as they claimed a 12th consecutive Premier League home win with a 4-0 rout of Bournemouth on Saturday to cut the gap to four points.
Arsenal ended their away hoodoo against Premier League title challengers with a 2-0 victory at Manchester City on Sunday that left Chelsea five points clear at the top.
Champions Manchester City will expect to get back to winning ways at home to Newcastle United in a match which pits Pep Guardiola against his fellow Spaniard Rafa Benitez.
Chelsea are 10 points clear at top of the English Premier League championship table.
Arsenal, Manchester City and Liverpool also joined Chelsea in the quarter-finals of the League Cup.
Chelsea will look to make amends after being runners-up to Leicester City and Arsenal in the last two seasons
LeicesterCity manager Claudio Ranieri hopes Chelsea midfielder N'Golo Kante will be given a warm reception when he returns to his old stomping ground for the first time since leaving the English champions.
David Silva came to the rescue of Manchester City with two goals in a 3-0 victory over Crystal Palace.