Pep Guardiola’s side looked set to drop points after Oriol Romeu cancelled out Kevin De Bruyne’s opener, only for Sterling to give City a 19th straight win in all competitions and a club-record 12th successive win in the league.It was Sterling’s third late winner in as many games and will have sickened second-place Manchester United, who had closed to within five points of the leaders by winning 4-2 at Watford on Tuesday.Elsewhere there were wins for Chelsea, Arsenal, Liverpool and upwardly mobile Burnley, while Wayne Rooney scored a hat-trick as Everton beat West Ham United 4-0 in front of Sam Allardyce, who is poised to become their new manager.Everton remain the last team to have avoided defeat against City, having drawn 1-1 at the Etihad Stadium in August, although Wolverhampton Wanderers took them to penalties in the League Cup.City went ahead in the 47th minute against Southamptom when Virgil van Dijk, under pressure from Nicolas Otamendi, diverted De Bruyne’s free-kick into his own net, with the Belgian midfielder awarded the goal.Romeu levelled with 15 minutes to play when Sofiane Boufal helped the ball into his path and the Southampton midfielder hammered a shot in off the crossbar.But with time almost…