Leaders Liverpool extended their advantage at the top of the Premier League to 11 points with victory over Brighton, as champions Manchester City surrendered further points in the title race.Centre-back Virgil van Dijk headed in twice in six first-half minutes for Jurgen Klopp's side, but their day was soured somewhat as goalkeeper Alisson received a straight red card for handling outside the area and Lewis Dunk caught the hosts off-guard with the resulting free-kick 11 minutes from time.In Saturday's early kick-off at St James' Park, Jonjo Shelvey's emphatic late strike earned Newcastle a 2-2 draw against Pep Guardiola's City.Kevin de Bruyne's equally brilliant 82nd-minute hit appeared to have salvaged victory after Jetro Willems had cancelled out Raheem Sterling's opener, but Shelvey's equaliser sees Manchester City move above Leicester to second on goals scored.Jose Mourinho's winning start to his reign as Tottenham manager continued as Dele Alli scored twice in Spurs' 3-2 home win against Bournemouth.A revitalised Alli struck either side of the interval for the hosts, who also had a Davinson Sanchez goal ruled out by the video assistant referee for handball.Moussa Sissoko added Tottenham's third to seal the win, before Harry Wilson responded with a late double for the visitors.Meanwhile, under pressure West Ham manager Manuel Pellegrini saw his side edge their west London derby against fourth-placed Chelsea.Left-back Aaron Cresswell scored the only goal three minutes after half-time, as Pellegrini's side ended their seven-game winless run in the league despite Michail Antonio having a goal ruled out by VAR.Roy Hodgson's Crystal Palace left Turf Moor with all three points as goals from Wilfried Zaha and Jeffrey Schlupp sunk Burnley.Zaha's well-taken finish in first-half injury-time was added to by Schlupp in the closing stages, with Burnley goalkeeper Nick Pope again beaten at his near post.