"I wanted to reach this record. To be able to reach this mark is an honour and against a team like Bayern it is even better," Ronaldo, who scored both goals, told BeIN Sport Spain.
Arturo Vidal headed Bayern into a first-half lead yesterday, but then skied a penalty attempt on the stroke of half-time before Ronaldo volleyed the defending champions' level.
Bayern played the last half an hour a man down after centre-back Javi Martinez was sent off for two fouls on Ronaldo within three minutes of each other.
"We believe we can still do it, we were the better team in the first half, could have made it 2-0 or 3-0," Neuer told ZDF.
More From This Section
But Bayern were outplayed in the second-half and most of Real's 23 shots on goal came after the break.
"We had everything under control in the first half, but didn't use the room consistently," said captain Philipp Lahm. "The tipping point was the red card."
- Tight security -
==================
There was a large police presence and inside the stadium there was polite applause when the announcer made reference to Dortmund's ordeal in the preceeding 24 hours.
Bayern suffered a blow before kick-off when top-scorer Robert Lewandowski, who has netted 38 goals this season, dropped out with a bruised shoulder and Thomas Muller deputised as striker.
Bayern were also missing injured Germany defender Mats Hummels against Real's formidable BBC attack - Gareth Bale, Karim Benzema and Ronaldo.
The Chile midfielder could have added a second when he headed Arjen Robben's cross wide of the post soon after.
Real made a poor start, rarely threatening Germany's goalkeeper Neuer, back after minor foot surgery a fortnight ago.
A strong drive from Ronaldo on 41 minutes which Neuer blocked having palmed a Benzema header onto the woodwork with 18 minutes played were their best first-half chances.
Vidal could have finished with a first-half hat-trick when he stepped up to take a penalty after Dani Carvajal's handball from a Franck Ribery shot.
It was a miss Bayern were soon to regret.
Real were level two minutes after the break when Carvajal found space on the right and fired in a cross which Ronaldo volleyed past Neuer.
Bale, who has laboured with an ankle injury recently, came off on 58 minutes and Real raised the tempo after he trudged off.
Having already picked up a yellow card for pulling Ronaldo back on 58 minutes, Martinez was shown a red for again fouling the Portugal captain just three minutes later.
Real's superstar then hit the winner as substitute Marco Asensio, on for Bale, put in a low pass for Ronaldo to tap the ball home between Neuer's legs.