Harry Kane and Leroy Sane
Harry Kane has made a brilliant start at Bayern Munich with three hat-tricks already to his name. Fabian Bimmer/Reuters

Harry Kane continued his brilliant start to life as a Bayern Munich player on Wednesday night when his two goals helped overcome Galatasaray in a 2-1 home win for the Bundesliga side in the UEFA Champions League.

This takes the Englishman's goal tally for his new club this season to 19 in all competitions and makes it four goals in as many games in the Champions League. It has simply been a breath-taking start at Bayern for Kane since departing Tottenham Hotspur in a big-money move this past summer.

Bayern came into Wednesday's game against Galatasaray with a 100 per cent record so far in the Champions League group stages, which included a 3-1 win away to Galatasaray in the reverse fixture in Turkey.

The Bundesliga giants had chances to go ahead in the first half through Jamal Musiala and Leroy Sane but both were ultimately unable to convert. Nothing could separate the two sides at the break whilst Musiala had to come off late in the first half after injuring his hamstring in a big blow to Thomas Tuchel's side.

Kane was inches away from putting Bayern ahead early in the second half as he hit the post from close range. Galatasaray thought they had taken the lead shortly after the hour mark as Lucas Torreira put the ball in the back of the net, but Mauro Icardi was deemed to be offside in the build-up to the goal.

It took until the 80th minute for the deadlock to be broken as Kane headed in from a free kick delivered by Joshua Kimmich. The goal was initially ruled out for offside, but VAR found there to be no issue and the goal rightfully stood.

The home side then doubled their lead just minutes later as they broke forward and substitute Mathys Tel played a low cross to the far post where Kane was free for a tap-in. The Turkish side pulled a goal back in stoppage time thanks to two of their substitutes combining, as Sergio Oliveira played a long ball over the top to Cedric Bakambu, who was able to finish first time past Manuel Neuer.

Bayern saw the game out with Kane proving to be the matchwinner for Tuchel's side and was awarded the Player of the Match award for his display. The victory over Galatasaray means Bayern will qualify from Group A as winners and already have safe passage into the knockout stages with two games to spare.

Other Group A participants Copenhagen and Manchester United played out a thrilling game on the same night with the Danish side coming out on top with a 4-3 win. Galatasaray will compete with those two sides to try and secure the other remaining qualifying spot for the knockout stages.

With Bayern having had unprecedented success domestically over the past decade, Kane was mainly brought in to bring success in the Champions League, and so far, he is showing he can deliver on this stage.

Outside of the Champions League, Kane has scored 15 goals in just 10 games for Bayern in the Bundesliga, which includes three hat-tricks. One of the hat-tricks came last weekend in Bayern's 4-0 away win against their main domestic rival of recent years, Borussia Dortmund.

However, despite Kane thriving in the Bundesliga so far, it has not been enough for Bayern to be top of the table, as Bayer Leverkusen remain two points ahead of them and is having a superb campaign under former Bayern player, Xabi Alonso.

Kane will be hoping he can win the first major trophy of his career this season and will be targeting the Bundesliga and Champions League, with Bayern already knocked out of the DFB-Pokal and having lost in the DFL-Supercup on Kane's debut this past August.

The striker's performances up to now for Bayern put him right up there as one of the best signings of the season, alongside fellow Englishman, Jude Bellingham, with the midfielder having a superb start at Real Madrid. Spurs' James Maddison and Arsenal's Declan Rice are two other English players to have made great starts at their new clubs.

The form of Kane is good news for England boss, Gareth Southgate, who will be hoping his captain and star striker continues his good run of form for next summer's UEFA European Championships which will be held in Germany.