Liverpool were the victims of an old-fashioned Atletico Madrid masterclass on Tuesday as Diego Simeone's side ground out a 1-0 win in Madrid to give themselves hope of reaching the Champions League quarter-finals.

Saul Niguez raised the roof at a bouncing Wanda Metropolitano by scoring in the fourth minute before Atletico's defence kicked in, suffocating the European champions and denying them a single shot on target.

"Tonight is one of those nights you don't forget," said Simeone. "We haven't gone through but we have beaten the best team in the world."

If Alvaro Morata had not slipped at the crucial moment, Atleti might even have taken a two-goal lead to Anfield, where they can expect an onslaught next month. 

If Liverpool remain favorites to go through, the roar from the Atleti fans at the final whistle, aimed at their fist-pumping players on the pitch, suggested Simeone's team now have belief.

Few had tipped them to keep this tie even alive for the second leg given their own stuttering form, in contrast to Liverpool, unbeaten in the Premier League, and gunning for a treble.

Jurgen Klopp said on Monday Atletico were a "results machine" but the temptation was to see his words as platitudes, not an accurate reflection of a side that sits 13 points behind La Liga leaders Real Madrid and had already lost six times this season.

Yet Atletico under Simeone have also become synonymous with upsetting the odds, just as they did when winning the Spanish title in 2014 and then twice reaching the Champions League final.

For all their failings this season, they summoned that spirit to produce a throwback performance full of tenacity, resilience and guts that was always going to be needed to give them any chance of success.

Elsewhere, the two most expensive players in the world were unable to outshine the prolific Erling Braut Haaland as the Norwegian sensation continued his remarkable rise by scoring both goals in Borussia Dortmund's 2-1 defeat of Paris Saint-Germain.

When Kylian Mbappe teed up Neymar to cancel out Haaland's opener in the second half of their Champions League last 16, first leg at the Signal Iduna Park, it looked like PSG would leave Germany with the upper hand in the tie.

But then, in the 77th minute, Haaland latched onto a pass from substitute Giovanni Reyna and sent a thumping left-foot shot rising high into the net from the edge of the penalty area to give Dortmund the advantage heading into the return leg in Paris on March 11.

Perhaps PSG's 402 million euro (434 million U.S. dollars) attacking duo will still make the difference in the return, and give the French club a place in the quarter-finals for the first time in four years.

But Dortmund deserved their victory on the night in a tie which only really began to live up to its billing in the second half, coming to life when Haaland pounced to score the opening goal from close range on 69 minutes after Thiago Silva blocked a Raphael Guerreiro shot.

If that was a typical poacher's finish, the winning goal was a demonstration of sheer brute force from the 1.94m tall, 19-year-old who now has 10 goals in seven Champions League games this season.  

"I feel like I still can do a lot better. I have to play better at this level, have to work hard to improve," Haaland told UEFA.com after being named man of the match.

"The result is quite a dangerous one, as Paris has a very strong team and can still go through in the return leg."