Champions Manchester City crashed out of the League Cup after suffering a shock 2-0 defeat at struggling Southampton in the quarter-finals on Wednesday.
Diogo Jota and Mohamed Salah were on target as Liverpool edged Premier League strugglers Nottingham Forest 3-2.
The two previous meetings at Anfield ended in 4-0 and 3-1 defeats for Arsene Wenger's Arsenal teams, but there is a fresh optimism around the club after a successful transfer window.
Images from the English Premier League matches played on Saturday night.
A preview of the line-up action in the English Premier League.
City host Crystal Palace in the league on Saturday, the only team they failed to score against last season while also losing 2-0 at home.
IMAGES from the English Premier League matches played on Saturday.
Crystal Palace's Wilfried Zaha has been subjected to racist abuse on social media and the forward shared screenshots ahead of Sunday's Premier League game at Aston Villa. The Ivory Coast international tweeted images of the messages he received from an individual on Saturday, which included one of members of the white supremacist organisation the Ku Klux Klan.
Premier League leaders Manchester United have agreed a fee to buy exciting young forward Wilfried Zaha from second-tier Crystal Palace, the clubs said on Friday.
Preview and timings of the Premier League matches this weekend
Crystal Palace manager Neil Warnock has mischievously blamed the club's Selhurst Park stadium announcer for his team's extra time 3-2 League Cup defeat by Newcastle United on Wednesday.
Manchester United kept up their chase for a Champions League qualification spot with Marcus Rashford and Anthony Martial on target in a 2-0 Premier League win over Crystal Palace, while Leicester secured a 2-0 home win over Sheffield United.
IMAGES from the English Premier League match played at Selhurst Park in London on Monday
Here is a compilation of some of the best photos from 2021...
Images from Sunday's action in the Premier League.
Liverpool's James Milner's converted a penalty on the stroke of half-time and Sadio Mane added a late second goal to secure a hard-fought 2-0 victory at Crystal Palace in the Premier League on Monday.
Images from the English Premier League matches played on Saturday.
Images from the English Premier League matches played on Saturday.
A round-up of the action in the English Premier League on Monday.
Images from Sunday's English Premier League matches.
Arsenal turned around its recent poor form to beat Leicester 3-1 on Sunday
A summary of Tuesday's action in the Premier League.
Fulham's home game against Brighton & Hove Albion on Wednesday has also been pushed behind closed doors, while West Ham United too will host Crystal Palace without spectators on the same day.
Crystal Palace set up a repeat of the 1990 FA Cup final against Manchester United after Yannick Bolasie and Connor Wickham securd a 2-1 victory over Watford at Wembley on Sunday.
Crystal Palace left Manchester City's hopes of retaining their Premier League crown in tatters after a 2-1 win at Selhurst Park on Monday to leave Manuel Pellegrini's side trailing a distant fourth in the title race.
City were due to open their season against Aston Villa and United against Burnley but those games will be moved.
Crystal Palace heaped more misery on Liverpool when they came from behind to win 3-1 in the Premier League on Sunday, six months after effectively ending the northern club's title hopes when they drew 3-3.
Images from Saturday's action in the Premier League.
Images from Sunday's Premier League action.
The defeat halted Brighton's impressive three-game winning streak which included a 4-1 win over Chelsea and a 3-1 victory at Arsenal in the League Cup on Wednesday.
"Tom Hopper, James Pearson and Adam Smith would like to convey their sincere apologies for their behaviour -- to the women involved in the incident, to the club and its owners, to the club's fans and to their families," a club statement said.
Sky Sports said that the 31-year-old Argentine was on his way to City's training facility in his car when the accident occurred.
Asafa Powell will take on fellow Jamaican Usain Bolt over 100 metres in what should be the highlight of the London Grand Prix on July 24, organisers said on Wednesday.
A round-up of Saturday's action in the Premier League.
Giroud scored with an improvised volley in the Premier League match on Jan. 1, producing an acrobatic flick with his left heel to convert Alexis Sanchez's cross into the net off the crossbar while tumbling forward.
Watford and Crystal Palace continued to inch towards Premier League safety after a scrappy goalless draw at Vicarage Road on Saturday that means the home side have taken just two points from a possible 21.
Match-by-match facts and statistics ahead of the first round of Premier League fixtures from August 5-7 (all times IST).
Leicester City's veteran striker Jamie Vardy came off the bench to break his long scoring drought and earn his side a 1-1 draw with a late equaliser
Premier League rejected Chelsea request to postpone Wolves game, says Tuchel.
Manchester City beat bottom club Sheffield United 1-0 to move three points clear of Manchester United who were held to a goalless draw at Arsenal in the Premier League on Saturday.