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.