Luton pulled one back on the half-hour mark when Chelsea keeper Kepa Arrizabalaga failed to keep out Jordan Clark's low effort which squeezed between his hand and leg into the net.
Another Liverpool great, Graeme Souness, said Klopp had produced a "fabulous" side.
Arsenal became the highest-profile casualties of the FA Cup third round as the 14-time winners lost 1-0 at Nottingham Forest, but Liverpool and Tottenham Hotspur avoided early exits after scares against lower-league sides on Sunday.
An 87th-minute header from defender Diego Llorente gave Leeds United a 1-1 home draw with Liverpool in the Premier League on Monday after the home side staged a protest against the breakaway Super League prior to the kickoff.
Barcelona striker Robert Lewandowski scored twice to set his side on course for a 5-0 Champions League thrashing of Swiss side Young Boys on Tuesday as the Catalan giants bounced back from a 2-1 loss at AS Monaco in their opener.
The match lived up to its billing right from the start
A brilliantly-worked goal by Ryan Christie and a Justin Kluivert penalty gave Bournemouth shock 2-0 Premier League win at home to 10-man Arsenal.
English Premier League champions Manchester City beat FA Cup winners Manchester United 7-6 on penalties to win the Community Shield.
Manchester City won an unprecedented fourth straight English top flight title with a 3-1 win over West Ham United.
IMAGES from the English Premier League matches played on Sunday.
Tottenham Hotspur and Liverpool raised the spirits with a rip-roaring 2-2 draw in a pre-Christmas Premier League classic on Sunday after a weekend marred by COVID-19 related postponements.
While Sunday's clash was the last time Klopp and Guardiola will face off for Premier League points, as far as this year's title race is concerned it merely made things even more interesting with Arsenal ahead of Liverpool on goal difference and City one point back. All three have 10 games left.
Liverpool striker Mohamed Salah has tested positive for the coronavirus on the eve of Egypt's Africa Cup of Nations qualifier against Togo, the Egyptian Football Association said on Friday.
The first leg, originally scheduled to be held at the Red Bull Arena in Germany, was shifted to Budapest after German authorities denied Liverpool entry into the country due to COVID-19 protocols.
Manchester City boss Pep Guardiola said he will miss his old sparring partner Juergen Klopp when the Liverpool manager calls time on his reign at the end of the season.
Images from Premier League matches played on Wednesday.
Thiago, 29, won the Bundesliga title in each of his seven seasons with Bayern and played in last month's Champions League final victory over Paris St Germain.
Images from the English Premier League matches played on Wednesday night.
Arsenal squeezed past Liverpool 5-4 on penalties to advance to the League Cup quarter-finals on Thursday after a goalless 90 minutes.
A round-up of Tuesday's action in the UEFA Champions League.
What makes Juergen Klopp's side such an unstoppable force?
Real Madrid fought back from two goals down as Vinicius Jr grabbed a hat-trick in a thrilling 5-2 win over visitors Borussia Dortmund in the Champions League.
Mohamed Salah hit a hat-trick as Liverpool humiliated Manchester United, romping to a stunning 5-0 victory at Old Trafford in the Premier League on Sunday that leaves Ole Gunnar Solskjaer's future in serious doubt.
Liverpool frustrated as they were forced to settle for a 1-1 draw at Brighton on Saturday
Liverpool may have to wait a little longer for their Premier League title celebrations after they were held to a 0-0 draw at Everton in the behind closed-doors Merseyside derby on Sunday.
Liverpool stayed in the hunt for a top-four Premier League finish with a 1-0 win at Wolverhampton Wanderers
"Indian travellers would be aware of recent disturbances in some parts of the United Kingdom. The High Commission of India in London is closely monitoring the situation," reads the message entitled 'Advisory for Indian Citizens Visiting the UK.'
Champions Liverpool were ripped apart 7-2 at Aston Villa and Manchester United were humiliated 6-1 at home by Tottenham Hotspur on Sunday in one of the most astonishing days of Premier League results.
British Prime Minister Keir Starmer has called an emergency COBRA meeting of senior ministers and police chiefs at 10 Downing Street in London on Monday after a weekend of riots across several cities in the country, which he termed a 'far-right thuggery' that will face the full force of the law.
The fixture was originally scheduled to be played on May 3 but was postponed after violent clashes between fans and police in which more than 100 supporters forced their way into the stadium and stormed the pitch to protest against the club's owners -- the Glazer family.
Liverpool forward Sadio Mane has become the second player from the English Premier League champions to test positive for COVID-19 this week.
Ronaldo back for Man Utd but injured Shaw faces weeks out
Roberto Firmino scored twice as Liverpool boosted their hopes of Champions League football next season
The battle for Champions League qualification continues with fourth-placed Aston Villa away to Luton Town on Saturday and Tottenham Hotspur, who are five points behind with a game in hand, hosting Crystal Palace.
Inspirational manager Juergen Klopp has rekindled the Anfield flame though and delivered the club's 19th top-flight title, one behind arch-rivals United's record of 20, after finishing runners-up to City in a thrilling race last season.
Chelsea kept alive their remote Premier League title chances with a 2-0 win over London rivals Tottenham Hotspur on Sunday, set on their way by an exquisite strike from Hakim Ziyech which was quickly followed up by a Thiago Silva header.
Twelve months ago Liverpool were ripping up the record books on the way to their first English top-flight title for 30 years but defeat by Everton on Saturday left them mulling a host of far less flattering statistics.
Liverpool's 30-year wait for their 19th English top-flight crown ended on Thursday when Manchester City lost at Chelsea and thousands of fans turned up at Anfield to celebrate.
A round-up of Sunday's action in the Premier League.
Only two teams -- Chelsea in 2005-06 and Manchester City last season -- have had more points after 18 Premier League games in a season than Liverpool's 48.