- Man Utd
Pierre-Emerick Aubameyang's lively debut was aided by three assists from Henrikh Mkhitaryan in his first Arsenal start.
Watford said Everton's approach for Marco Silva had been "the catalyst" for the decision.
Everton signed England winger Theo Walcott from Arsenal in a deal worth a reported 25 million pounds ($34 million, 28.3 million euros) on Wednesday.
Walcott, who has scored 108 goals in 397 matches for Arsenal, is surplus to requirements at the Emirates Stadium having made just 16 appearances this season.
Saturday's late kick-off saw England forward Kane score his 98th Premier League goal and surpass Teddy Sheringham's previous club record of 97.
The 24-year-old England midfielder has signed a five-and-a-half-year contract and will wear the number eight shirt.
Liverpool had led 1-0 at the break after James Milner converted from the penalty spot but Everton looked to have secured a replay when Gylfi Sigurdsson equalised midway through the second half.
Ross Barkley is out of contract at Goodison Park at the end of this season, after rejecting a new deal with Everton.
Jose Mourinho's side were holding onto a slender lead given to them by Anthony Martial when Lingard took possession with nine minutes left at Goodison Park.
Wayne Rooney's hat-trick was instrumental in Everton registering their 2nd win from 13 matches.
Alexis Sanchez's late penalty gave Arsenal a controversial win over Burnley, while managerless Everton endured more misery against Southampton.
Arsenal succumbed to a 62nd-minute penalty from Sehrou Guirassy after the French striker tumbled to ground inside the area under a challenge from Mathieu Debuchy.
Jack Wilshere, overlooked by England manager Gareth Southgate earlier in the day, had the best chance for Arsenal but saw a second-half effort cleared off the line.
Liverpool's defeat -- their first in 10 league games against Spurs -- also saw them become only the sixth team to have conceded over 1,000 goals since the Premier League was launched in 1992.
While Ronald Koeman will be relieved to avoid a fifth defeat in Everton's last six Premier League games, the Toffees once again looked poor for long periods and remain without an away win since January.
Now, Coleen, 31, who is pregnant with her fourth child, has revealed that she will be eating her own placenta as it offers a nutritious boost to mothers post delivery.
Arsene Wenger made nine changes to the Arsenal team after they travelled to eastern Europe on the back of a 2-0 win over West Bromwich Albion in the Premier League on Monday.