Real Madrid overcame Atletico in the Champions League final because coach Carlo Ancelotti was able to adjust his tactics and go on the attack in time to rescue the game while his opposite number Diego Simeone had no cards left to play
Ancelotti fielded a cautious starting lineup at Lisbon's Stadium of Light, with Sami Khedira in a deep-lying central role despite having only recently returned from knee surgery, and Real were outplayed for long periods in the first half.
Atletico deservedly went ahead when Diego Godin outjumped a sluggish-looking Khedira and nodded the ball over a stranded Iker Casillas in the 36th minute and they looked comfortable with their lead well into the second period.
Ancelotti responded with around half an hour remaining by hauling off Khedira and left back Fabio Coentrao and replacing them with attacking midfielder Isco and zippy fullback Marcelo.
The tone of the match changed immediately, with Real pushing forward relentlessly and carving out a number of half-chances and Atletico forced deeper and deeper.
Although Atletico looked like they might hold on and secure their first continental triumph to add to this season's La Liga title, Sergio Ramos leaped to head a superb leveller in the third minute of added time.
The Atletico players were stunned, with several falling to the ground in disbelief, and their fans packed into one end of the stadium fell eerily silent as extra time loomed.
Ancelotti's Atletico counterpart Simeone had been forced to use the first of his three substitutes as early as the ninth minute when Diego Costa limped off and was replaced by Adrian.
Costa was a surprise inclusion in the starting lineup after picking up a hamstring injury last weekend and the sight of him leaving the pitch so early marked Simeone's first error in the night's tactical battle.
Simeone had used his two remaining substitutions by the end of regular time, with Filipe Luis limping off with what looked like cramp, and most of the Atletico players looked utterly spent as extra time began.
Real sensed victory was within their grasp and played with renewed energy, with Marcelo and the excellent Angel Di Maria attacking down the left with Cristiano Ronaldo and Gareth Bale down the right.
Atletico, with no outlet up front, were hanging on, hoping for penalties and there was a sense of the inevitable when Bale, Real's record signing, made it 2-1 in the 110th minute with a back-post header.
Atletico were done and dusted and barely raised a challenge as Marcelo danced through and added a third before Ronaldo's penalty with almost the last kick of the match after the Portugal forward was tripped.
It was a triumph for Ancelotti, who in his debut season at Real becomes only the second man alongside Liverpool's Bob Paisley to win the European Cup three times.
He has delivered the 10th continental crown the world's richest club by income have been chasing since their last title in 2002 and succeeded where the likes of Jose Mourinho and Manuel Pellegrini before him had failed.
Real also won the King's Cup, beating Barcelona 2-1 in the final, and were on course for a rare treble before their La Liga faltered in the final weeks - Atletico triumphing in that battle.
"It was difficult and we suffered tonight but I think we deserved it," Ancelotti said in an interview with Spanish television.
"We believed that we could level the game and it went well for us after that," added the Italian, who won the European Cup with AC Milan twice as a player and twice as a coach and was calmness personified despite the increasingly tense nature of Saturday's encounter.
For Atletico and Simeone, it was a cruel and deflating end to an astonishing season, when they won their first domestic league title since 1996 and emerged as genuine contenders among Europe's elite despite limited resources.
It was also a case of history repeating itself as Atletico were within a minute of winning the 1974 European Cup final before Bayern Munich equalised and won the subsequent replay.
"This match is not worth crying about, when the players have given everything they could on the pitch," Simeone told Spanish TV.
"Now they need to rest, relax and take things calmly," added the former Argentina captain.
"I am very proud of my players, my staff, we have competed with one of the great clubs with humility."
There was precious little humility on show at the death, however, as the hot-headed Argentine raced on to the pitch in a fury to confront Real defender Raphael Varane.
Simeone, who also gave remonstrated with the referee on the pitch during extra-time, had to be restrained by the Atletico players and coaching staff before eventually being dragged clear to look on from afar as Real began their celebrations.