Harry Kane scored a hat-trick as Bayern Munich thumped Mainz 8-1 on Saturday, equalling a 60-year-old record and keeping alive his team's hopes of catching leaders Bayer Leverkusen.

Kane, who also laid on two assists, now has 30 goals in his first season in Munich colours, matched the record for a maiden campaign set by German legend Uwe Seeler for Hamburg in 1963-64.

With nine games remaining to break the record, the England captain has also drawn nearer to the season record of 41 goals set by Bayern's Robert Lewandowski in 2020-21.

The win was Bayern's second biggest this season, just behind their 8-0 demolition of Darmstadt in October.

Midfielder Leon Goretzka, who scored a double, said: "It was a convincing win -- the kind we've missed this season."

Bayern are now seven points behind Xabi Alonso's unbeaten Leverkusen, who host lowly Wolfsburg on Sunday.

"It's our duty to keep giving it everything we've got," Goretzka said. "If Leverkusen get shaky, we've got to be there."

Having sealed their progression to the Champions League quarter-finals on Tuesday with a 3-0 home win over Lazio, Bayern were direct and decisive against Mainz.

Outgoing manager Thomas Tuchel said midweek Bayern needed to "win, win, win" to have any chance of catching Alonso's side and Kane obliged early, tapping in a Jamal Musiala pass after 13 minutes.

Kane had a header saved seven minutes later, but Leon Goretzka was on hand to knock in the rebound.

Nadiem Amiri wove an incredible free kick through Bayern's defence shortly after but England striker Kane restored Bayern's two-goal lead in first-half stoppage time, collecting a lofted Goretzka pass on the turn and blasting home.

Thomas Mueller added a fourth early in the second-half to break Mainz's resistance, allowing Bayern to run riot, with further goals to Musiala, Serge Gnabry, Kane and Goretzka to bring the tally to eight.

Kane, who arrived from Tottenham in the summer, also became the first player to score four hat-tricks in a Bundesliga season.

The loss leaves Mainz in second last, nine points from safety. Sporting director Martin Schmidt lamented his side's openness, saying "we wanted to be courageous, but we were too courageous".

Elsewhere, RB Leipzig won 2-0 at home over last-placed Darmstadt to leapfrog Borussia Dortmund into fourth, the final guaranteed Champions League spot.

The hosts rebounded from a frustrating Champions League last 16 exit to Real Madrid on Wednesday, forcing Darmstadt into an own goal from Thomas Isherwood after three minutes.

Marco Rose's men added another through Christoph Baumgartner early in the second-half to go two points clear of Dortmund, who play at Werder Bremen in Saturday's late game.

"We're looking only at ourselves," said sporting director Rouven Schroeder. "When we win our games, we'll qualify for the Champions League."

Third-last Cologne drew 3-3 at derby rivals Borussia Moenchengladbach, having led twice in a feisty encounter.

Cologne led for over an hour but were forced to come from behind late in the game when Robin Hack scored two goals in three minutes to give the home side the lead.

Damion Downs levelled the scores with 11 minutes remaining but Cologne will finish the round in 16th, the relegation play-off spot, seven points from safety.

Jeffrey Gouweleeuw scored the only goal as Augsburg beat Heidenheim at home to climb out of a crowded mid-table to eighth place, within touching distance of the European spots.