The Spain international buried two first-half headers to put Carlo Ancelotti's side 3-0 up on aggregate before Cristiano Ronaldo scored his 15th goal in this season's tournament to wrap up the win and break Lionel Messi's record for strikes in one campaign.
Ronaldo then drilled a free kick under the wall in the dying minutes of the match to cap a perfect night for the Spanish giants, who will now face Chelsea or Atletico Madrid in their first Champions League final since 2002.
The only disappointment from a wonderful evening for Real came in the 38th minute, as playmaker Xabi Alonso was booked for a rash tackle on Bastian Schweinsteiger, meaning he will miss the final.
Bayern goalkeeper Manuel Neuer presented Real with an early opportunity as his clearance from a ball over the top went straight into the path of Gareth Bale - restored to the starting XI after illness - however, the Welshman could only fire high over the crossbar.
But it did not take long for Ancelotti's men to make the crucial breakthrough, which came in the 16th minute when the unmarked Ramos met Luka Modric's perfectly placed corner with a bullet header.
And just four minutes later, Real doubled that advantage to take control of the tie as Pepe flicked Angel Di Maria's right-wing free kick towards Ramos, who netted his second goal of the game with a diving header.
Bayern did finally threaten the Real goal midway through the first half, Franck Ribery flashing an effort across the face of goal, but the visitors’ threat on the counter was perfectly illustrated shortly after by a fine break from Ronaldo, although the Portuguese could only fire wide from the edge of the area.
The hosts failed to heed the warning offered by Ronaldo, though, and he duly netted his milestone goal by coolly finishing off a scintillating team move that saw Bale charge through the heart of the Bayern defence before laying the ball off for the 29-year-old.
Ronaldo then went close with an audacious effort from 40 yards following another botched Neuer clearance.
Bayern were allowed more of the ball following the restart but struggled to break down a determined and organised Real defence. Arjen Robben curled an effort narrowly wide from the edge of the area, before Toni Kross lashed a decent effort just over the bar.
However, a miserable night for Bayern coach Pep Guardiola was capped off in the 90th minute, as Ronaldo drove a low 20-yard free kick under the wall for his 16th Champions League goal of the campaign that ends Bayern's chances of winning a second straight treble.