Bale’s right-footed shot ricocheted off City midfielder Fernando on its way into the top corner to break the deadlock in the tie in 20th minute, with Madrid going on to dominate the encounter despite failing to add to their lead.
The 1-0 aggregate result, after last week’s goalless first leg stalemate, set up a mouthwatering final on May 28 between Real and their city neighbours Atletico Madrid, who they beat to lift their 10th European crown in 2014.
“The players deserve this,” said Madrid boss Zinedine Zidane, who has the chance to crown his first season as coach with club football’s most coveted prize.
“Everyone worked hard and that’s why we’re in the final. I’m delighted for what has happened. The final will be perfectly even, but now we’re going to enjoy this, it’s an important day.”
For City, however, it was a tame ending to their European campaign as they failed to force Madrid keeper Keylor Navas into a single save.
While Bale enjoyed good fortune in forcing the goal, the Wales international nonetheless produced a blockbuster European performance.
He tirelessly closed down City’s midfield in a lung-busting display and was Madrid’s biggest threat in attack, providing exquisite passes and sending a header crashing against the bar in the second half.
City’s chances of shutting out Madrid were stung when their influential captain Vincent Kompany limped off the pitch with what appeared to be a muscle problem in the ninth minute, capping a frustrating season overshadowed by injuries for the centre back.
Madrid seized the moment soon after. The energetic Dani Carvajal skipped past Kevin De Bruyne down the right and slipped the ball round the back of City’s defence and into the path of Bale.
He made for the near post before his cross spun off the outstretched leg of Fernando and looped into the net off the woodwork.
Madrid grew stronger after the goal and a shot from Ronaldo flew over the bar, while Pepe put the ball in the net only to see his effort ruled out correctly for offside.
Despite Madrid’s dominance, City could have levelled just before the break when De Bruyne found Fernandinho on the left of the area, and the Brazilian’s left-footed shot clipped the near post.
It was one of few scares for Madrid, who bossed the second half as they did the first.
Ronaldo spurned three chances to double the lead and Bale’s header smashed the bar.
“We could easily be in the final but they managed the game well, and got a very lucky goal,” said City keeper Joe Hart.
“They’ve beaten us with a very lucky goal but it is what it is.”