Ibrahimovic and Lukaku, who played together at Manchester United, exchanged words at the end of the first half before the pair had to be restrained as the players left the pitch for the interval.
Champions Manchester United will travel to Swansea City for their first English Premier League match under new manager David Moyes, while Manuel Pellegrini's Manchester City are at home to Newcastle United on August 17.
Manchester City reached the League Cup final after recovering from a shaky start as Sergio Aguero's brilliant header sealed a 3-1 win over Everton in the semi-final second leg to clinch a 4-3 aggregate victory.
United are 16th in the standings with a game in hand heading into the international break.
There were a few nerves at the end but Liverpool set up a Champions League semi-final with Spain's Villarreal after Roberto Firmino scored twice in a 3-3 second-leg draw with Benfica on Wednesday to ensure a 6-4 aggregate win.
English Premier League leaders Liverpool will need to maintain their excellent recent record against Everton in Sunday's Merseyside derby if they are to hold their advantage over second-placed Manchester City.
Liam Delap, the son of former Stoke City defender Rory, scored the opener for Pep Guardiola's side in the 2-1 win at the Etihad Stadium
The injury to the Chile forward, who was left out of the squad for Tuesday's Champions League victory over Young Boys, "will require further investigation to confirm its severity", the club added.
Chelsea slipped up in their push for a Champions League spot when they lost 1-0 at home to Arsenal in the Premier League on Wednesday with Emile Smith Rowe's first-half goal settling the London derby after a defensive mix-up by the hosts.
Real Madrid failed in their attempt to sign France striker Kylian Mbappe from Paris Saint Germain on the final day of the transfer window as Cristiano Ronaldo completed his move from Juventus to Manchester United.
Tottenham Hotspur brutally exposed Liverpool's defensive frailties as Harry Kane plundered two more goals in his side's 4-1 romp at Wembley on Sunday.
Jose Mourinho's side have been the most impressive of any of the title contenders.
IMAGES from the English Premier League matches played on Saturday.
Wolves midfielder Leander Dendoncker then hit the post with a powerful shot before Portuguese winger Podence made it 2-0, meeting Pedro Neto's cross from the right with a superb cushioned volley in the 27th minute.
Harry Kane's 101st Premier League goal was the difference as Tottenham Hotspur earned a 1-0 win over Arsenal, to continue their fine recent form in north London derbies in front of a Premier League record crowd at Wembley on Saturday.
Manchester United eased the pressure on manager Ole Gunnar Solskjaer with a 3-1 win at Everton in the Premier League on Saturday with Bruno Fernandes scoring twice and Edinson Cavani grabbing his first for the club.
IMAGES from Saturday's English Premier League matches.
Leaders Manchester City kept up their unbeaten run with a 3-1 win over Bournemouth on Saturday. Manchester United salvaged a 2-2 draw at Southampton, who sacked manager Mark Hughes on Monday.
Skipper Robin van Persie scored a hat-trick as Arsenal beat Chelsea 5-3 after twice coming from behind in a remarkable Premier League match of attacking brilliance and defensive mistakes at Stamford Bridge on Saturday.
Zlatan Ibrahimovic's 28th goal of the season in all competitions put United ahead and Sunderland's cause became all but impossible after Seb Larsson was sent off close to halftime.
Match-by-match facts and statistics ahead of the Premier League fixtures on April 28-30
Manchester City have completed the signing of midfielder Jack Rodwell from Everton on a five-year contract, the Premier League champions said on Sunday.
A preview of the line-up action in the English Premier League.
Romelu Lukaku scored for Chelsea in a 5-1 FA Cup third-round victory
"When he has the ball at his feet, he can make things happen for himself and he can make things happen for other players. He is a very special player."
England head into Euro 2020 with a new factor for manager Gareth Southgate to deal with -- high expectations.
With United unable to sign a replacement, the pressure will be on 21-year-old England forward Marcus Rashford to deliver the goals in a more central role than he has previously operated in.
Images from the English Premier League matches played on Wednesday night.
Follow the latest developments from all the on-field and off-the-field action in the Premiership.
Mauricio Pochettino's Tottenham Hotspur can cement their status as the top dogs in the capital if they end an eight-year wait and defeat Arsenal in the North London derby on Sunday.
Arsenal's Aubameyang compared to Henry after his derby double
In Pep Guardiola's 100th match in charge of the Manchester club, captain De Bruyne led from the front as City outclassed the Gunners, who have now suffered six home games without a win. Images from the EPL matches played on Sunday.
Manchester City tightened their stranglehold at the top of the Premier League on Wednesday by trouncing bottom club West Bromwich Albion 3-0 as nearest rivals Manchester United suffered a chastening 2-0 defeat at Tottenham Hotspur.
Manchester City produced a blistering first-half performance to win 4-1 at Sunderland in the League Cup third round on Tuesday, inflicting more misery on Dick Advocaat's struggling side.
Everton have been handed the dubious distinction of being the 'dirtiest' Premier League team after a study on the all-time cards and fouls by www.dirtyteams.co.uk.
High drama ensued during the English Premier League matches on Wednesday as Spurs manager Jose Mourinho was booked while Brighton stunned Chelsea via Alireza Jahanbakhsh's superb equaliser to deny the Blues victory. Here is all the EPL action in IMAGES from Wednesday's matches.
British media reported that the fee for the 24-year-old would be around 75 million pounds ($96.68 million), making him the club's second most expensive signing after last year's world record deal for French midfielder Paul Pogba.
Premier League champions Chelsea eased past a disappointing Everton with goals from Spaniards Cesc Fabregas and Alvaro Morata sealing a 2-0 victory on Sunday.
Willian's late strike snatched a 1-0 home win for Chelsea over a stubborn Everton side to maintain lead.
News of all that's transpired on and off the football field
