Arsenal took the lead in the opening minute when Gabriel Martinelli latched onto Martin Odegaard’s through ball to beat Alisson.
Darwin Nunez scored from close range 11 minutes from halftime following a pass from Luis Diaz, who had to limp out of the game before the break, and Bukayo Saka took advantage of five minutes of injury time to put Arsenal back in front from Martinelli’s pass.
Roberto Firmino drew Liverpool level again in the 54th minute after a pass from Diogo Jota, but Jota then became the villain when he conceded a 76th minute penalty that allowed Saka to net the winning goal.
The win keeps Arsenal a point ahead of Manchester City, who continue to score goals with ease, as they brushed Southampton aside 4-0 on Saturday.
Joao Cancelo and Phil Foden put Man City 2-0 ahead before halftime, before Riyad Mahrez and Erling Haaland finished the scoring in the second half.
Harry Kane’s 33rd-minute header from a Son Heung-min cross keeps Tottenham third after a 1-0 win away to Brighton, who played well but lacked a cutting edge and saw their best chances denied by Hugo Lloris.
Chelsea continue to improve under Graham Potter and had an easy 3-0 win at home to struggling Wolves, for whom former Chelsea striker Diego Costa failed to make an impression.
Wolves defended well in the first half, but Kai Havertz put Chelsea in front in injury-time, before Christian Pulisic and Armando Broja sealed the win with strikes in the 54th and 89th minutes.
Manchester United ended a decent week by coming from behind to win 2-1 away to Everton, who took a fifth-minute lead through Alex Iwobi’s curing shot.
Antony equalized with his third goal in three games 10 minutes later, and Cristiano Ronaldo, who replaced the injured Anthony Martial, scored a left-footed winning goal a minute before halftime.
West Ham are also improving after a slow start to the season, with goals from Jarrod Bowen, Gianluca Scamacca and Michail Antonio scoring for David Moyes’ side after Andreas Pereira had put Fulham ahead.
Crystal Palace got a much-needed win with Odsonne Edouard and Eberechi Eze seeing them overturn Pascal Struijk’s opener for Leeds United, who have now gone five games without a victory.
Bruno Guimaraes scored twice as Newcastle United won 5-1 at home to Brentford, with Jacob Murphy and Miguel Almiron also scoring for Newcastle, who had help from Ethan Pinnock’s own goal.
Ivan Toney’s penalty against his former club was scant consolation for the visitors.
Leicester City remain deep in trouble after surrendering a 1-0 lead away to Bournemouth, who overcame Patson Daka’s 10th minute opener with strikes from Philip Billing on 67 minutes and Ryan Christie four minutes later to stretch their unbeaten run to five games.
