Curtin Jones's 71st-minute strike saw Liverpool edge past Everton in a derby tie at Anfield.
Manchester City had a late goal from Gabriel Jesus ruled out by VAR video review as they drew 2-2 at home to Tottenham Hotspur on Saturday -- their first league home game without victory in nearly eight months.
Spurs beat Ajax 3-2 in the second leg of the semi-final on Wednesday and will face Liverpool on June 1 in Madrid.
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.
Images from Sunday's Premier League action.
Lucas Moura scored twice as Tottenham Hotspur romped to a 3-0 English Premier League win over Manchester United at Old Trafford on Monday as Jose Mourinho's team's defensive frailties were brutally exposed once again.
'We said we had 45 minutes to give everything. I'm a fan first and foremost and I know how much it means to the club'
'Without Harry Kane many people were talking about Sonny (Son Heung-min) but today it was Lucas Moura who scored three goals and you know if you don't respect all the players, you cannot only have 11 players'
Mason Greenwood's late winner earned Manchester United a 1-0 win at wasteful Wolverhampton Wanderers in the Premier League on Sunday, breaking the record for the longest unbeaten away run in English Football League history in the process.
It looked as though substitute Harry Kane's late penalty had put Tottenham into the quarter-finals but fellow substitute Davies fired home to provoke joyous scenes at Spotland.
In a thriller at Anfield, a weakened Liverpool side came back from the brink to beat Leicester City on penalties after a 3-3 draw, setting up a semi-final against Arsenal.
United youth product Gomes, 18, struck after Spurs' Lucas Moura cancelled out Anthony Martial's first-half opener and gave the 20-time Premier League champions another victory after they beat Perth Glory, Leeds United and Inter Milan.
Reaction to Tottenham Hotspur's last-gasp 3-2 Champions League semi-final win over Ajax Amsterdam.
'We saw Liverpool last night. It goes to show it's not over until it's over. Disappointed with the first leg, how we started and we started like that tonight. But after the break we came out'
Holders Manchester City were eliminated from the League Cup by West Ham United after a penalty shootout at London Stadium on Wednesday, ending Pep Guardiola's team's four-year domination of the competition.
Harry Kane netted his 200th goal for Tottenham Hotspur as they won 3-1 at Ludogorets and AC Milan's 24-match unbeaten run ended
Images from Sunday's action in the Premier League.
Jorginho's first-half penalty earned Chelsea a 1-0 victory over Tottenham Hotspur in the Premier League on Thursday.
A summary of Sunday's action in the Premier League.
His goal completed a comeback after Cristiano Ronaldo put Juventus 2-1 in front.
Images from Sunday's action in the Premier League.
An early Mohamed Salah penalty and a late strike by Divock Origi gave Liverpool a 2-0 win over Tottenham Hotspur in Saturday's all-English Champions League final
Arsenal turned around its recent poor form to beat Leicester 3-1 on Sunday
Chelsea beat Eintracht Frankfurt on penalties on Thursday to set up an all-English Europa League final with local rivals Arsenal in Baku on May 29.
Manchester City chalked up yet another victory to maintain their stranglehold of the Premier League title race but pursuers Manchester United and Leicester City both secured important wins to enhance their top-four bids on Sunday.
Images from the English Premier League matches played on Saturday.
Video footage showed Tottenham's Eric Dier climbing over seats and confronting a home fan before he was restrained by security guards and other fans. He was eventually led away.
Federico Valverde finished off a stunning move in extra time to give Real Madrid a 3-2 victory over arch-rivals Barcelona
Brazil forward Lucas scored his first goal for Paris St Germain to help the Ligue 1 champions snatch top spot with a 2-0 win at Girondins Bordeaux.
Manchester City moved back to second in the Premier League after a stylish 3-0 win over Everton at the Etihad Stadium on Sunday as Pep Guardiola's side responded to convincing Chelsea and Liverpool wins with a reminder of their class.
Manchester United and Tottenham Hotspur built hefty leads with emphatic away wins in their Europa League last 32 first-leg matches but AC Milan were held to a 2-2 draw at Red Star Belgrade as the competition resumed on Thursday.
Premier League Leeds United suffered the biggest upset of the FA Cup third round when they fell to a 3-0 defeat by fourth-tier Crawley Town on Sunday
Steven Bergwijn scored twice in stoppage time as Tottenham Hotspur stunned Leicester City and pulled off a remarkable 3-2 victory in the Premier League on Wednesday.
'It's a nightmare, like a dream that went bad'
Angel Di Maria volleyed in with 15 minutes left to give Paris Saint-Germain a 1-0 win at Stade Rennais on Friday and extend their lead at the top of the Ligue 1 table to 10 points.
A round-up of Saturday's action in the Premier League.
A preview of the line-up action in the English Premier League.
Images from Sunday's action in the Premier League.
Jose Mourinho, sacked by Manchester United last season after his reign there turned sour, has been charm personified since swapping punditry for the Tottenham job.
Zlatan Ibrahimovic struck a last-minute winner to put Paris St Germain in the French League Cup final with a 2-1 win at Nantes on Tuesday having opened the scoring as they boosted their hopes of a maiden domestic double.