Premier League sides cruised into the EFL Cup third round on Tuesday, but there was concern for Brighton over new signing Matt O'Riley.

Denmark midfielder O'Riley arrived from Celtic this week but lasted just nine minutes of his Seagulls debut, hobbling off with an apparent ankle injury against League One side Crawley Town.

That issue will leave Brighton head coach Fabian Hurzeler worried, though the performance from the rest of his side left little concern after a 4-0 victory.

Simon Adingra got things going in the first half before Jeremy Sarmiento, Julio Enciso and Adam Webster were on target after the interval in a routine second-round win.

In stark contrast to Brighton, Sean Dyche's Toffees are yet to win – or score – in the Premier League this season but dispatched League Two's Doncaster Rovers 3-0 at Goodison Park.

Tim Iroegbunam and Iliman Ndiaye both scored their first competitive goals for Everton before backup striker Beto sealed a routine victory, which came in similar fashion to Palace's 4-0 win over Norwich City.

Oliver Glasner's side are without victory in the top flight this campaign, too, but eased into the third round after Jean-Philippe Mateta scored twice, along with goals for Eberechi Eze and Daichi Kamada, at Selhurst Park.

Leicester City, another side without a point to their name in the top division yet, also overcame Tranmere Rovers 4-0 thanks to goals from new signing Jordan Ayew, Stephy Mavididi, Wilfred Ndidi and Harry Winks.

The EFL Cup third round will see Premier League champions Manchester City host Chelsea while holders Liverpool will play League One Derby County at Anfield.

Erik ten Hag's Manchester United are set to welcome Aston Villa to Old Trafford and there is another enticing all-Premier League clash between Nottingham Forest and Tottenham.

Brighton and Hove Albion will travel to Mikel Arteta's Arsenal as one of the seven games to feature two top-flight teams facing each other.

League Two Crawley knocked out Premier League Fulham on Tuesday, and they are rewarded with a visit to Championship outfit Burnley.

Meanwhile, last season's Europa League semi-finalists West Ham United will face second-tier Blackburn Rovers.

EFL Cup third-round draw in full:

Stevenage v Charlton, Leicester City v Newport County, West Ham United v Blackburn Rovers, Wolves v Leeds United, Nottingham Forest v Tottenham, Manchester United v Aston Villa, Bournemouth v Everton, Liverpool v Derby County, Burnley v Crawley Town, Bristol City v Lincoln City, Manchester City v Chelsea, MK Dons v Morecambe, Newcastle United v Crystal Palace, Southampton v Sheffield Wednesday, Arsenal v Brighton and Hove Albion, Brentford v Gillingham.

Ties will be played week commencing November 7.

Leeds United suffered an FA Cup shock on Sunday as the Premier League side lost 3-0 to Crawley Town, for whom television star Mark Wright made his debut.

Marcelo Bielsa's men became only the second top-flight team to lose by at least three goals to a fourth-tier side in the competition since the English Football League added the bottom division in 1958.

The last side to suffer such a result was Oxford United, who lost by the same scoreline against Aldershot Town in January 1987.

Crawley, who are sixth in League Two, had lost their three previous FA Cup matches with Premier League teams, against Manchester United, Stoke City and Reading, while they had not reached this stage of the competition in eight years.

Nick Tsaroulla scored a fine opener 50 minutes into what was just his seventh appearance in senior football, and Ashley Nadesan doubled the lead three minutes later following an error by goalkeeper Kiko Casilla.

Jordan Tunnicliffe netted a deserved third for Crawley, for whom Wright, best known for his work in English reality TV series The Only Way Is Essex, made a late substitute appearance.

Leeds have now been knocked out of the cup at this stage for the past four seasons, their worst run since another four-campaign stretch from 2003-04 until 2006-07.