Liverpool produced its best performance since the arrival of new manager Juergen Klopp to beat Premier League title chasers Manchester City 4-1 on Saturday. A stunning first-half display of high pressing and counterattacking saw Klopp's side surge into a three-goal lead at the Etihad Stadium. It was the first time since February 2003 that City had conceded three before the interval in a league fixture. "It was very, very good. We took our chances and made brilliant goals in the counterattack," Klopp said. "With results like this the boys will start to believe in themselves and that's very important," Klopp added following a result that moves his side to within six points of a Champions League berth. First-half goals from Brazilian duo Philippe Coutinho and Roberto Firmino stunned the host which had fallen behind after Eliaquim Mangala put through his own net. Firmino enjoyed his best performance in a red shirt since joining the club from German side Hoffenheim for a reported fee of 29 million pounds ($45.8 million). And he was flanked by compatriot Coutinho, who continues to thrive under Klopp. The pair were involved in all three goals as Liverpool established a firm hold on the game. Fit-again striker Sergio Aguero pulled one back shortly before the interval, curling a splendid effort beyond Liverpool goalkeeper Simon Mignolet. Substitute Christian Benteke was also denied by Hart after being played through by Jordan Ibe. From the resulting corner defender Martin Skrtel thumped in the fourth as Liverpool registered its biggest win of the season. Former Liverpool forward Raheem Sterling was ineffective in his first game against his former side following his acrimonious summer move away from Anfield. City slipped to third on 26 points, two adrift of new league leader Leicester, while Liverpool moves up to ninth with 20 points. Bayern extends Bundesliga lead Javi Martinez made the breakthrough for Bayern Munich to extend its German league lead with a 3-1 win at Schalke Saturday, when all Bundesliga games were played amid increased security measures. David Alaba put Bayern ahead in the ninth minute when his powerful shot took a huge deflection. Max Meyer equalized against the run of play eight minutes later. Leroy Sane eluded Xabi Alonso and passed to Meyer, who cut inside Philipp Lahm and fired past Manuel Neuer inside the far post. Bayern extended its lead to eight points over Borussia Dortmund, which slipped to a 3-1 defeat at Hamburger SV Friday. Juventus beats AC Milan Juventus continued to climb up the Serie A table as it beat AC Milan 1-0 to string together three consecutive Serie A wins for the first time this season. Paulo Dybala scored the only goal in a sellout at the Juventus Stadium Saturday. Earlier, Mattia Destro came back to haunt his old side as he scored a late penalty to help Bologna draw 2-2 against title-chasing Roma in Serie A. Roma moved provisionally level on points with table-topping Fiorentina and Inter Milan, while Bologna inched two points clear of the relegation zone. Juventus leapfrogged Milan, moving a point above the Rossoneri and six below the top three. — Agencies