Liverpool claimed the bragging rights in the Merseyside Derby following a 2-0 victory over Everton in the Premier League at Anfield on Saturday.
Arsenal secured their first victory over Everton in six years following their hard-fought 1-0 victory at Goodison Park in the Premier League on Sunday.
Chelsea and Everton progressed to the next round of the League Cup after narrowly avoiding humiliating exits against AFC Wimbledon and Doncaster Rovers on Wednesday evening.
Leicester City and Leeds United were relegated from the Premier League while Everton won to stay up on the final day of the season on Sunday.
A brace by Ilkay Gundogan put Manchester City within touching distance of the Premier League title following their comfortable 3-0 victory over Everton at Goodison Park on Sunday.
Christian Eriksen could make his long awaited return for Manchester United while Luke Shaw has been ruled out for their upcoming Premier League clash against Everton on Saturday afternoon.
Arsenal suffered a shock 1-0 defeat to Everton to deny their Premier League title hopes, while Liverpool's woes continued following their 3-0 loss at Wolves.
Struggling side Everton have announced the appointment of former Burnley boss Sean Dyche as their new manager to replace the sacked Frank Lampard.
Everton have sacked manager Frank Lampard after spending less than a year in charge at the struggling Premier League club.
Pep Guardiola was left frustrated after his side dropped valuable points following their 1-1 draw to Everton at the Etihad Stadium on Saturday.