It was yet another frustrating and horrifying result in Europe for Paris Saint-Germain.

With less than half an hour to go at the Santiago Bernabeu stadium, everything seemed to be going according to plan.

Last summer the French giants refused to accept Real Madrid's offer to buy Kylian Mbappe, who is out of contract in three months, and had invested heavily in an ageing Lionel Messi and Sergio Ramos and also in promising Italian goalkeeper Gianluigi Donnarumma.

Mbappe scored to give the high-flying PSG a 1-0 win in the first leg of the Champions League knock-out tie. The wonder kid then impressed as PSG dominated the first hour of the second leg in Madrid, scoring in the 39th minute, putting his team two goals up.

Then PSG pressed the self-destruct button.

Donnarumma, trying to play out of defense, passed to Vinicius Junior who found Karim Benzema for a tap-in. The Madrid talisman followed the act by hitting three in 17 minutes and PSG were utterly shell-shocked in a tie they had dominated.

Eventually, the team that historically finds a way to win in the Champions League, even when they should lose, beat the team that so often manages to lose when they should have won.

All eyes were on Mbappe, who was the only player to be cheered by Madrid's fans before the game as they were gifted an up-close preview of the player they hope will be theirs this summer.

For an hour, Mbappe looked at home at the Bernabeu. He had already had two shots saved and an effort that hit the net ruled out for offside when he ran onto Neymar's first-time pass after 39 minutes. He froze the terrified David Alaba and then whipped a shot past goalkeeper Thibaut Courtois.

His best moment came with an outrageous step-over to beat Courtois and net in the second half only to be ruled offside again.

Then PSG's defence unravelled and Mbappe was reduced to a mere spectator as one of the Madrid pensioners he is slated to replace stole the show.

After the final whistle, Messi, who just won the men's Ballon d'Or award for a record-extending seventh time in November, stood frozen, stunned in Bernabeu. Watching the celebrations was the last thing the Argentine superstar wanted to do as PSG capitulated to Madrid.

"We paid dearly for our mistakes at the end," PSG captain Marquinhos said. "It's tough to explain."

"We didn't manage our emotions well. We left ourselves exposed," PSG coach Pochettino observed. "We leave with great pain and disappointment because we didn't score the goals to reflect our superiority over the two games."

Pochettino also fumed at referee Danny Makkelie for not whistling for a foul as Benzema challenged Donnarumma before Madrid's first goal.

"Explaining what happened is easy, there was a foul on Donnarumma during the first goal, and that changed everything," he said. 

"The worst feeling is that we were the better side," Pochettino added. "But we lost the tie in 10 minutes."

This isn't why one of the greatest players of all time came to PSG. Nor why so much was invested in linking the 34-year-old genius up with Neymar and Mbappe.

The wait for a first Champions League title goes on for PSG after 11 years of Qatari ownership and more than $1 billion in transfers. 

Whichever managers come and go, PSG too often looks like a group of players masquerading as a team.

There will be recriminations at PSG. "We were convinced we were the better side," PSG sporting director Leonardo insisted. "It's a big blow. We have to accept our mistakes and our inability to handle difficult situations. We lost and there are things to analyse."

In sharp contrast, Benzema was in delirum. At 34 years old, he is the oldest player to score a hat-trick in Champions League history.

"We know PSG like to have the ball. We started well, we tried to score and in the second half we won the match with our mental strength," he said. "Every game is a final now for us in the Champions League and La Liga but today we showed that Real Madrid is alive."

The sentiment was echoed by Madrid coach Carlo Ancelotti.

"We won a very difficult game, which got a lot more complicated after Mbappe's goal," he said. "We suffered a lot. Then we pushed higher which was what we wanted to do."

"We scored the first goal and from there everything changed. The fans pushed us and we believed more, more and more. It was a spectacular night."

(With input from agencies)