With Atletico poised to win the trophy for the first time after going ahead with a first-half Diego Godin header, Real struck back after relentless pressure with a Sergio Ramos header in the third minute of added time from a Luka Modric corner.
That sent the final into extra time and, with a tiring Atletico almost out for the count after taking a battering for most of the second half, Real scored three times in 10 minutes.
World record signing Bale headed them in front after 110 minutes, Marcelo made it 3-1 following a solo run eight minutes later before Ronaldo, the Portugal captain playing in his capital city, converted a penalty with almost the last kick.
That was his 17th goal of the Champions League campaign, an all-time record for one season, and meant Carlo Ancelotti became the second coach to win the European Cup three times after Bob Paisley's Liverpool triumphs in 1977, 1978 and 1981.
Italian Ancelotti also won the trophy twice as a player with AC Milan in 1989 and 1990, while Real became the first team to score four goals in the final since Milan's 4-0 win over Barcelona in 1994.
"Yes that was just incredible, what can I say, it was our aim from the start of the season," Ancelotti told reporters. "It was such a hard game and Atletico were such powerful opponents, but I think we deserved it in the end.
"We scored in extra time. We believed that we could win the game and it went well for us in the end. Everyone did well and what they could and we finished drained, exhausted but very, very happy. Were we lucky to score so late? I don't think so, I think we deserved it."
In contrast Atletico coach Diego Simeone was ordered off the field by referee Bjorn Kuipers for running on to the pitch after Atletico went 4-1 down, but he was much calmer when he faced the media later, walking in to applause at the news conference.
The Argentine said he was angry because Real defender Raphael Varane flicked the ball at him but added that he should not have acted as he did. "At that point it was pointless for the player to create that situation," he said.
"After a 4-1 scoreline maybe it was pointless for me to get angry. But if you analyse the whole match Real Madrid were better in the second half, they pinned us in our own half and we could not move."
For Atletico the evening evoked painful memories of the last time they reached the final in 1974 when they were leading Bayern Munich in Brussels only for Georg Schwarzenbeck to equalise in the last minute of extra time to force a 1-1 draw and a replay which Bayern won 4-0 two days later.
This time Atletico were almost as close to glory and a Champions League and domestic league double but instead Real secured a Champions League and Spanish Cup double as Ancelotti's first season in charge ended in absolute joy for their fans at the Stadium of Light and utter dejection for Atletico's.
A header from Bale 20 minutes into extra time turned the match a month after the Welshman scored the winner with a stunning solo goal in a 2-1 King's Cup triumph over Barcelona.
His latest goal repaid a further chunk of the 100 million euros ($136.31 million) Real paid Tottenham Hotspur to secure his signature last August and all but killed off any hope the flagging Atletico players had of winning the match.


Latest News from Sports News Desk