The results saw both Bayern and Leipzig strengthen their positions near the top of the Bundesliga, although Elversberg and Hamburg were left to reflect on disappointing defeats.

Kane delivers as Bayern survive Elversberg test

Harry Kane scored the decisive goal as Bayern Munich held on for a 2-1 victory away to Elversberg to extend their unbeaten start to the season to six matches in all competitions.

Elversberg, enjoying their first Bundesliga campaign, started confidently after winning their opening two matches. Bayern, however, showed their quality when Lennart Karl tested goalkeeper Nicolas Kristof with a long-range effort after combining with Kane.

The visitors eventually took the lead shortly before the half-hour mark. Ismael Saibari's low cross reached Karl at the far post and the youngster calmly finished from close range.

Elversberg thought they had found an immediate response when Cole Campbell fired past Jonas Urbig, but the goal was ruled out for offside.

Campbell was subsequently replaced by Maurice Krattenmacher, who had joined Elversberg from Bayern during the summer. The 21-year-old wasted little time making an impact against his former club.

After Kane had another effort ruled out for offside, Krattenmacher found space on the edge of the box and curled a superb right-footed shot into the top corner to level the match.

Bayern responded strongly. Michael Olise twice came close to restoring the lead, with one effort cleared off the line before another attempt looped onto the crossbar.

Kane eventually settled the contest in the 72nd minute.

The England captain received the ball in a crowded area, used two composed touches to create room and fired past Kristof at the near post.

The goal was Kane's fourth in competitive action this season and lifted Bayern to fourth place, while Elversberg slipped to sixth.

Leipzig run riot against struggling Hamburg

RB Leipzig continued their outstanding home form with a commanding 5-0 victory over Hamburger SV at the Red Bull Arena.

The win was Leipzig's seventh consecutive Bundesliga home victory, setting a new club record.

Leipzig dominated the early stages and took the lead after 17 minutes. Ezechiel Banzuzi broke down the right before delivering a low cross towards Tidiam Gomis, who finished first time through the narrowest of gaps at the near post.

Hamburg's defensive problems continued as they conceded for the 17th consecutive Bundesliga match.

Leipzig doubled their advantage before the half-hour mark when Antonio Nusa won possession from Shafiq Nandja well inside the Hamburg half. Nusa drove towards the box and his effort deflected off a recovering defender before beating Daniel Heuer Fernandes.

Hamburg failed to register a shot on target during the first half but had an opportunity to reduce the deficit early after the break. David Moller Wolfe collected a loose ball inside the area, only for Maarten Vandevoordt to save his near-post effort.

Leipzig remained in control and came close to adding a third when Christopher Nkunku met Gomis' chipped cross but headed wide.

The hosts then finished the match in ruthless fashion, scoring three times in five minutes.

Willi Orban headed in Nusa's free-kick at the far post before Nkunku found the bottom-right corner from inside the area.

Romulo Cardoso completed the rout after dispossessing Warmed Omari, rounding Heuer Fernandes and rolling the ball into an empty net.

The victory lifted Leipzig eight places to fourth, while Hamburg dropped to the bottom of the table after a third straight defeat. Merlin Polzin's side are still waiting for their first goal and point of the campaign.

Harry Kane rescues Bayern as Leipzig crush Hamburg