Liverpool substitute Curtis Jones and Everton midfielder Abdoulaye Doucoure were also shown red cards after the game, and the final whistle sparked a scuffle between both sets of players.
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.
Cristiano Ronaldo came off the bench to earn Manchester United a hard-fought 2-1 victory at Everton in the Premier League on Sunday, taking his career goal tally to 700 in the process.
IMAGES from EPL matches played on Thursday.
New Everton boss Sean Dyche's reign began with a shock 1-0 victory over English Premier League leaders Arsenal.
Everton secured their English Premier League status as Dominic Calvert-Lewin scored five minutes from time to snatch a thrilling 3-2 victory over Crystal Palace after they rallied from two goals down at a rocking Goodison Park on Thursday.
'We always knew it was going to be an important one playing against a quality side, but I think it affected us a little bit too much.
Images from the English Premier League matches played on Sunday.
Images from the English Premier League matches played on Saturday
Images from Saturday's Premier League matches.
IMAGES from the EPL matches played on Saturday.
Images from EPL matches played on Wednesday.
Ross Barkley scored a sublime goal as Everton beat Queens Park Rangers 3-1 at Goodison Park on Monday to subject the travel-weary Londoners to their eighth away defeat in as many Premier League matches this season.
IMAGES from the English Premier League match played between Everton and Manchester City on Wednesday
Everton striker Romelu Lukaku struck a late equaliser to salvage a 1-1 draw against a solid CrystalPalace side in an absorbing Premier League match at Goodison Park on Monday.
Kane began the night level on 19 goals with Liverpool's Mohamed Salah in the race for the Golden Boot.
Images from Saturday's action in the Premier League.
The London club dominated the first half but fell behind to a superb goal from their former winger Aaron Lennon before young midfielder Dele Alli furthered his case for a place in England's midfield with a classy equaliser just before the break.
News of all that's transpired on and off the football field
IMAGES from Premier League matches played on Sunday.
IMAGES from the EPL matches played on Tuesday
Leicester City's Premier League title defence got off to a terrible start as they were beaten 2-1 at promoted Hull City, who shrugged off an injury crisis to shock the champions on the opening day of the new season on Saturday
Images from Saturday's action in the English Premier League.
IMAGES from the English Premier League matches played on Saturday.
Premier League heavyweights Liverpool and Manchester United were caught by late sucker punches in two games that finished far more dramatically than they began on Sunday.
Tottenham Hotspur boss Andre Villas-Boas has been criticised for allowing France international goalkeeper Hugo Lloris to play on despite briefly losing consciousness against Everton on Sunday.
James Rodriguez netted twice and Dominic Calvert-Lewin became the first Everton player to score in the opening four matches of a Premier League season as they beat Brighton & Hove Albion 4-2 on Saturday to stay top of the table with a maximum 12 points.
Rodriguez whipped Everton in front from the edge of the box, and Michael Keane and Calvert-Lewin ensured it was two wins from two in the Premier League so far this season.
Manchester United eased the pressure on manager Ole Gunnar Solskjaer with a 3-1 win at Everton in the Premier League on Saturday with Bruno Fernandes scoring twice and Edinson Cavani grabbing his first for the club.
IMAGES from the English Premier League matches played on Saturday
Images from the English Premier League matches played on Saturday
Images from the English Premier League matches played on Wednesday
IMAGES from Saturday's English Premier League matches.
United down Newcastle after Saints stun Chelsea on a dramatic night in the English Premier League.