Manchester United's new signing Alexis Sanchez scored on his home debut in a 2-0 win over Huddersfield Town as they took advantage of a slip by cross-town rivals and Premier League leaders Manchester City on Saturday, Reuters reported. After City had been held 1-1 at Burnley, their daunting lead over United was reduced to 13 points when Jose Mourinho's side eventually overcame a defensive Huddersfield side. It took 55 minutes before Romelu Lukaku broke the deadlock after which Sanchez won a penalty, had it saved by Jonas Lossl, but tucked away the rebound in the 68th. City paid the price for missed chances as they drew at Turf Moor with Johann Berg Gudmundssonâ€TMs 82nd minute equaliser earning Burnley a point. City had dominated possession but, after taking the lead with a fine strike from Brazilian Danilo in the 22nd minute, the visitors failed to press home their advantage. Raheem Sterling produced one of the misses of the season from two metres out and Burnley made the most of that let-off. City have 69 points from 26 games, ahead of United on 56 with third-placed Liverpool (50) at home to Tottenham Hotspur (48), who are fifth, on Sunday, while Chelsea (50), in fourth, visit mid-table Watford on Monday. Huddersfield's defeat at Old Trafford dropped them into the bottom three for the first time since being promoted as Southampton and Swansea City both moved above them. Bottom club West Bromwich Albion lost 3-2 at home to Southampton on an emotional day at the Hawthorns, where there was a minute's applause for the home side's former striker Cyrille Regis, who recently died aged 59. Albion led early on through Egyptian defender Ahmed Hegazi but were rocked by three goals in a quarter of an hour either side of halftime. Southampton held on after Salomon Rondon's goal to secure a first win in 13 league games, leaving Albion four points adrift at the bottom with 20 points. Improving Swansea earned a valuable point with Federico Fernandez's equaliser, at Leicester City, for whom Jamie Vardy scored his 13th goal of the season, in all competitions. Bournemouth consolidated their place in the top 10 by coming from behind to beat Stoke City 2-1 and, on a good day for the south-coast sides Brighton & Hove Albion beat West Ham United 3-1 to draw level with them on 27 points.