Real Madrid's Galacticos just don't know when they are beaten. Manchester City just keep on making the same mistakes.

Jude Bellingham's stoppage-time goal sealed a stunning comeback for Madrid and a 3-2 lead in their Champions League playoff against City.

In six frantic minutes at the end of a breathless first leg on Tuesday (Wednesday AEDT), the Spanish giants scored twice to take a precious advantage into next week's match at the Bernabeu.

City led 2-1 after 80 minutes at the Etihad Stadium through goals in each half from Erling Haaland. But Brahim Diaz and Bellingham silenced the home crowd and extended a sorry record for City that has seen them concede seven goals in the last 15 minutes of Champions League games this season.

Bellingham slid in to convert Vinicius Junior's lobbed pass in the second minute of added time and clinch victory.

At least City have a chance to salvage the tie in the second leg, but the sense of deflation was clear after such a late collapse.

"It's not the first time, unfortunately, it happened many times and that's why it's difficult," City manager Pep Guardiola said.

It was another thrilling, white knuckle-ride of a game between these two giants of European soccer, and a one-goal advantage for Madrid means there is still plenty to play for.

Defeat ended City's 35-game unbeaten run at home in the Champions League, dating back to 2018.

City led through Haaland's goal in the 19th minute. By that stage, Madrid had had a penalty overturned for offside and a Ferland Mendy goalbound effort blocked by Manuel Akanji.

Vinicius Junior then hit the bar with a curling shot and Akanji also clipped the frame of the goal with a header.

Haaland hit the bar again early in the second half.

Madrid equalised on the hour through a freakish goal from Mbappe when his miskicked volley wrongfooted Ederson and looped softly over the line.

The Frenchman hit the post again, before Ceballos brought Phil Foden down just inside the box and Haaland's penalty restored City's lead.

On came former City academy player Diaz, who left City for Madrid in 2019, and he levelled the game again before Bellingham's winner.

In other results, Paris Saint-Germain beat Brest 3-0, Juventus won 2-1 against PSV Eindhoven, and Borussia Dortmund notched a 3-0 win at Sporting Lisbon.

Ousmane Dembele struck twice for PSG in Guingamp, France, to extend his scoring streak to 10 games in a row. His outstanding form has seen him score 18 goals during that run.

It was his shot that led to PSG taking the lead through a 21st-minute penalty after Pierre Lees-Melou handled in the area. Vitinha converted the spot kick.

Dembele scored his first in the 45th minute when he broke free down the right and curled a shot inside the post. His second came in the 66th when he pounced on a loose ball to score his 23rd goal of the season.

Substitute Samuel Mbangula grabbed a late winner for Juventus. The 21-year-old Belgian forward reacted quickly when goalkeeper Walter Benitez spilled a low cross from the right by Francisco Conceicao in the 82nd minute.

Juventus took the lead late in the first half from Weston McKennie's powerful strike into the top corner from just inside the penalty area.

Veteran midfielder Ivan Perisic calmed the home fans with a fine finish in the 56th minute.

Meanwhile, Serhou Guirassy scored his 10th Champions League goal of the season as last year's runners-up Borussia Dortmund beat Sporting Lisbon 3-0.

Guirassy scored one goal and set up another for Pascal Gross as Dortmund scored twice in eight minutes.

Karim Adeyemi finished off a rapid counterattack to score Dortmund's third in the 82nd minute.