Harry Kane scored twice as Tottenham Hotspur won 3-0 at home to Bournemouth on Sunday to cut Premier League leaders Leicester City's advantage back to five points. But Manchester City's title ambitions were dealt a likely fatal blow in a 1-0 home defeat by Manchester United in which Manuel Pellegrini's side lost both Joe Hart and Raheem Sterling to injury. The result, courtesy of 18-year-old striker Marcus Rashford's 16th-minute strike, left City 15 points behind Leicester in fourth place and took Louis van Gaal's United to within a point of the Champions League places. Leicester had provisionally gone eight points clear with a 1-0 win at Crystal Palace on Saturday, but it took Kane just 43 seconds to settle Spurs' nerves against Bournemouth at White Hart Lane by sliding in to convert Kyle Walker's cross. It was the England striker's 20th goal of the campaign and he made it 21 in the 16th minute by applying a polished finish to Dele Alli's pass. Kane was denied a hat-trick by Bournemouth goalkeeper Artur Boruc in the 52nd minute, but Christian Eriksen followed in to score and seal a win that lifted Spurs six points above third-place local rivals Arsenal. City are four points further back in fourth place and while they, like Arsenal, retain a game in hand on the pace-setters, their title challenge now appears over. Rashford was United's match-winner at the Etihad Stadium, the youngster skinning the hapless Martin Demichelis and planting a shot past Hart in the 16th minute to become – at 18 years and 141 days – the youngest scorer in the fixture's 171-game history. Sterling hobbled off with an apparent groin injury midway through the first half and Hart was stretchered off with a suspected calf problem early in the second half to complete a miserable day for manager Pellegrini, whose side are also under threat from West Ham United. But it was a rare day to remember for under-fire United manager Van Gaal, whose team ended a four-game winless run to rekindle their hopes of Champions League qualification. MITROVIC RESCUES NEWCASTLE Earlier, Aleksandar Mitrovic scored an 83rd-minute equaliser as Newcastle United prevented northeast rivals Sunderland from escaping the relegation zone in a 1-1 draw at St James' Park. Seeking a seventh successive win over Newcastle, Sunderland took the lead in the 44th minute when Jermain Defoe volleyed home left-footed after Rob Elliot had parried a shot from Fabio Borini. But with seven minutes remaining, Georginio Wijnaldum crossed for Serbian striker Mitrovic to score with a downward header, sparing Newcastle manager Rafael Benitez from defeat in his first home game and keeping both teams in the bottom three. "The players fought till the end and the fans were behind us in a difficult situation," said Benitez. "We have to do this from the first minute to the last to get more points. I think we can stay up." In the day's other early game, Sadio Mane scored twice – and squandered a penalty – as Southampton checked Liverpool's charge towards the top four by storming back from 2-0 down to win 3-2 at St Mary's. Jurgen Klopp's Liverpool went 2-0 up inside 22 minutes, Philippe Coutinho curling in a fine effort from 25 yards and Divock Origi teeing up Daniel Sturridge to score. Senegal international Mane, a halftime replacement for Dusan Tadic, saw a penalty saved by Simon Mignolet early in the second half after Martin Skrtel was adjudged to have fouled Graziano Pelle. But Mane sped past Mamadou Sakho to reduce the arrears and after Pelle equalised with a vicious shot in the 83rd minute, the Italian freed Mane to run through and score an 86th-minute winner. "The first half we played brilliant football," said Klopp. "We have to close the game out. You have to accept that in the second half they controlled the game."