The match in Lisbon ended 1-1 after regular time. Diego Godin put Atletico in front but Sergio Ramos got a stoppage-time equaliser to send the match into extra-time, when Gareth Bale, Marcelo and Cristiano Ronaldo all added to the scoreline.
Atletico suffered a blow earl on when key man Diego Costa had to be replaced after just nine minutes after succumbing to injury.
The first moment of anticipation came when Cristiano Ronaldo had an opportunity from a free-kick, but his low, dipping effort didn't trouble Thibaut Courtois in the Atletico goal.
Real threatened first when Angel Di Maria went on a surging run down the left, beating two players before being cynically brought down by Raul Garcia, who was booked for a professional foul. Sergio Ramos took exception to the foul and protested too far, earning himself a booking too.
Bale had the best chance of the first half for Real when he intercepted a loose pass from the back, drove forward with Atletico's defenders all on the back foot, dummied his shot, but could not find the finish onto the bottom-left corner he was looking for.
Atletico took the lead before half-time thanks to a goalkeeping blunder by Real legend Iker Casillas. A free-kick was played onto the penalty spot and cleared out to Juanfran, who knocked it back into the area. Casillas came out to claim but then changed his mind, and before he could backtrack Godin's looping header was bouncing over him and over the line before he could keep it out.
Ronaldo had another direct free-kick attempt early in the second half but Courtois was equal to it and pushed it over for a corner.
Atletico created a few half-chances as they looked for a second goal but nothing of consequence as Real dominated possession. Carlo Ancelotti sent Isco and Marcelo onto the pitch to give his side more attacking impetus as they went in search of an equaliser.
Atletico were looking dangerous going forward and playing some great football before Ronaldo had his best chance of the night. Sergio Ramos won the ball back in midfield, played a one-two and sent a teasing cross into the area as the Portuguese powered in, but he could not get enough on the ball as it glanced off his head.
In the 67th minute Isco had a chance on the edge of the area but scuffed his shot wide of the left-hand upright as Real turned up the pressure on Atletico's goal.
Six minutes later Bale had a sight of goal on the edge of the area but snapped at his shot, getting good power behind it but sending it wide of the right-hand upright. Ronaldo tried a spectacular overhead kick moments later but was under pressure and could not keep his effort down.
In the 77th minute Bale went on a direct run at goal from the right flank under pressure from an Atletico defender but after getting into the box, the former Tottenham Hotspur man could only slice a shot with the outside of his left foot wide of the near post when perhaps the right foot would have been the better option.
Moments later Isco showed some brilliant skill to bring down a right-wing cross with his back to goal, turning in the same movement, but he was crowded out before he could get his shot away on the six-yard line.
Real continued to pepper the Atletico goal in the closing stages but bodies were being put on the line and vital defensive intentions made as coach's side repelled their attacks.
In stoppage time Sergio Ramos dragged Real back into the match after finding space in the box to head Luka Modric's corner into the bottom-left corner and force extra time.
1-1 it ended after regular time.
Ronaldo had his third free-kick attempt in the first half of extra time but hit the wall, with Real's top scorer frustrated after his handball appeal was waved away by the referee.
Real looked more dangerous during extra time and got the reward their endeavour deserved in the 110th minute when Di Maria broke through two defenders down the left and into the box. The Argentine's shot was blocked by Courtois but only as far as Bale at the far post as he got up to nod home to put Real into the lead.
Marcelo made it 3-1 as a tired Atletico defence allowed him too much space outside the box and the Brazilian drove forward before hitting a powerful shot underneath Courtois and into the net.
Real were awarded a penalty late on and Ronaldo was all too keen to step up and smash in his 17th goal in this season's Champions League campaign – a European record for a single season.
