Haaland scored a first-half double to take his tally to 52 goals in just 50 games in the competition as City stretched their unbeaten run to five games.

But the visitors were pegged back in the 90th minute when Dier converted from the spot after being kicked in the head by Nico Gonzalez.

Norway’s Haaland had not had a touch of the ball in the first 15 minutes but with his first, he latched on to Josko Gvardiol’s dinked pass and lobbed a cool finish over the advancing Philipp Kohn.

But Jordan Teze equalised just three minutes later with a thunderbolt strike from outside the area, which arrowed into the top corner and gave Gianluigi Donnarumma no chance.

City, though, were controlling the possession and Phil Foden came close to regaining the lead when he shifted the ball on to his weaker right foot but smashed his shot against the crossbar.

Haaland was on the periphery of the game but showcased his ruthlessness by leaping high above Mohammed Salisu and powerfully heading in from Nico O’Reilly’s cross on the stroke of half-time.

Donnarumma made a sharp save low down to deny Maghnes Akliouche in the second half, but the Italy goalkeeper could not stop Dier’s late spot-kick.

The 29-year-old England international has been out of favour under Spurs boss Ange Postecoglou, making only four Premier League appearances this season.

Dier said the move was a “dream come true” and added, “as a child you want to play for a club like Bayern one day”.

Spurs have also completed the signing of Genoa centre-back Radu Dragusin for around £25m.

Bayern have the option to sign Dier for a further year after the loan contract ends.

He added: “Bayern is one of the biggest clubs in the world and has an incredible history.

“I want to help the team with my versatility in defence. I’m really looking forward to my new teammates and the fans at the Allianz Arena, which in my eyes is one of the best stadiums in the world.”

Dier will join former Tottenham and England team-mate Harry Kane at 32-time Bundesliga champions Bayern.

Their boss Thomas Tuchel said in a news conference on Thursday: “He’s a specialist at centre-back, he has also played as a six in the Premier League, but not any more for a long time.

“We’re getting him for the centre-back position – he can play right or left centre-back as well as in a back three.”

Dier, who only has six months left on his current Spurs deal, has been capped 49 times by England but struggled to claim a first-team place for Tottenham this season.

Manager Postecoglou said his side could afford to lose Dier, despite problems in his defence.

Cristian Romero and Micky van de Ven have both suffered with injuries this season and Postecoglou has played full-backs Ben Davies and Emerson Royal in central defence in recent weeks to cover gaps in the backline.

Dier joined Tottenham in a £4m deal from Portuguese side Sporting Lisbon in 2014 and has made 274 Premier League appearances, but started only one league game this season.

Spurs have already been active in the transfer window, bringing in former Chelsea striker Timo Werner on loan from RB Leipzig and Romanian Dragusin from Genoa, with full-back Djed Spence heading in the other direction to Italy as part of a 25m euros (£21.5m) deal.

Tottenham, fifth in the Premier League, are next in action on 14 January at Manchester United.

Bayern sporting director Christoph Freund said: “We’re pleased we’ve been able to sign Eric Dier. He’s long been in our thinking for this transfer window.

“Eric will be a valuable part of our defence. His sporting abilities and international experience will help the team both on the pitch and in the changing room.”

Bayern are second in the Bundesliga, four points behind leaders Bayer Leverkusen but with a game in hand.

They entertain Hoffenheim on Friday and have another home league game against Werder Bremen on Sunday, 21 January.