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The interesting team news came on the Atletico side as Diego Simeone opted for Stefan Savic over Jose Gimenez and also selected Augusto Fernandez ahead of Carrasco. Fernando Torres and Griezmann were both included, however, in what was a formation that matched up to Real Madrid.
Real Madrid had a golden chance to take the lead in the sixth minute when Casemiro met a whipped free kick from Bale, but somehow Jan Oblak kept out the midfielder's effort from barely five yards out.
Referee Mark Clattenburg might well have produced three or four yellow cards in the opening 10 minutes due to the nature of the contest, but it took until the 11th minute for the first booking to be shown as Dani Carvajal felled Griezmann.
Real Madrid were rewarded for their fast start in the 15th minute of action when Ramos tapped home from close range after Bale had flicked a Toni Kroos free kick towards the danger zone.
Atletico, who wanted offside on the Ramos opener, just could not settle as the first period gathered pace and it was Los Blancos that continued to threaten on the counter-attack, with Ronaldo and Bale both fired-up at the San Siro.
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Benzema had a half-chance in the 32nd minute after finding space in a wide position, but Oblak was on hand to make another smart save and prevent his side from falling 2-0 behind.
Griezmann struck one for Atletico in the 34th minute as Simeone's side enjoyed a rare venture forward, but it was comfortable for Navas, who had a very comfortable first period in Milan.
Griezmann was the player making things happen for the Red and Whites and the France international again hit one from distance five minutes before the interval, but his effort was never really troubling Real Madrid's Costa Rican stopper.
Atletico actually shaded the possession in the first period and led Real Madrid 3-2 when it came to attempts on target, but there was no question that Zidane's team deserved to take a lead into the interval.
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Atletico had a golden chance to level moments into the second period when Pepe brought Torres to the ground inside the box, but Griezmann smashed his resulting spot kick against the crossbar.
It was a clumsy challenge from Pepe and the correct decision from Clattenburg, but Griezmann went for power and the ball rattled the woodwork and allowed Real Madrid to keep their one-goal lead intact.
Atletico had another super opportunity in the 54th minute when Savic met a loose ball inside the Real Madrid box, but the centre-back could only force his effort wide of the post.
Real Madrid continued to ride their luck as the hour mark approached and a close-range volley from Saul Niguez just missed the post during another spell of pressure from Simeone's side.
Real Madrid should have scored a second on the counter-attack 20 minutes from time when Benzema drove into the Atletico box, but Oblak was once again on hand to make a smart save and keep the score at 1-0.
Oblak was again called into action in the 78th minute to keep out a strike from Ronaldo, before Savic blocked a goal-bound strike from Bale. That block from the centre-back proved crucial as from the resulting counter, Carrasco fired a Juanfran cross home from close range to level the contest.
Both teams had chances in the minutes that followed, but Torres could only fire wide from close range, before Bale brought a smart save from Oblak at his near post.
Neither could find a second goal, however, as the final followed the same route as the 2014 contest between the two teams - extra time after a 1-1 draw in 90 minutes.
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Ronaldo had the standout chance of the first period of extra time, but the Portuguese could only head straight at Oblak after finding space inside the Atletico box.
The chances continued to arrive at both ends of the field, with Griezmann and Carrasco coming close for Atletico and Bale looking the most likely to score a second for Real Madrid.
As expected, the energy levels continued to dip as the 120-minute mark approached and the contest finished 1-1, leaving a penalty shootout to determine who would be crowned 2016 winners of the Champions League.
Lucas Vasquez, Griezmann, Marcelo, Gabi, Bale, Saul and Ramos all netted in the shootout, but Juanfran missed Atletico's fourth, which allowed Ronaldo to step forward and win the contest for the team in white.