Manchester City improved their prospects of Champions League qualification with a 5-0 demolition of Crystal Palace, while Swansea City’s 1-0 win over Everton pushed Hull City into the Premier League relegation zone on Saturday.

Frustrated by damaging draws in their previous two games, City got back on track and climbed to third in the table after a stylish display inspired by David Silva’s return from injury at Eastlands.

Silva, out for a fortnight after suffering a blow to his knee during the FA Cup semi-final defeat by Arsenal, opened the scoring after two minutes.

Vincent Kompany doubled City’s lead in the 49th minute before Kevin De Bruyne’s long-range strike made it three 10 minutes later.

Raheem Sterling’s cool finish in the 82nd minute was followed by Nicolas Otamendi’s diving header in stoppage time as City leapfrogged Liverpool on goal difference.

Pep Guardiola’s side also moved four points clear of fifth-placed Manchester United as the battle to finish in the top four heats up.

The Premier League is tough

United, who travel to Arsenal, and Liverpool, who host Southampton, are both in action on Sunday.

“Today was important because we are playing for the future of the club,” Guardiola said.

“The Premier League is tough. There are four amazing teams fighting for the final two places in the top four.”

Palace’s third successive defeat left them four points above the relegation zone and still not certain to stay up.

At the KCOM Stadium, already-relegated Sunderland won 2-0, securing their first victory in 11 games to leave Hull in severe danger of joining them in the Championship next season.

Hull boss Marco Silva had been unbeaten in his previous 41 home league games, a record dating back to his time in charge of Portuguese side Estoril in 2014 and encompassing spells with Sporting Lisbon and Olympiakos.

Having taken 19 points from a possible 21 at home during his four months as Hull boss, it was a shock to the Portuguese coach when his side fell behind in the 69th minute.