Viktor Kassai, who officiated the game, was guilty of incorrectly showing red to Arturo Vidal for a fair challenge and allowing two offside goals scored by Cristiano Ronaldo.
The victory at the Santiago Bernabeu Stadium put Madrid into the semifinals for the seventh straight season and kept alive its hopes of becoming the first team to retain the Champions League title since the competition's new format was created in 1992.
"In the big moments, Ronaldo always comes through", Madrid coach Zinedine Zidane said.
Correction: This article originally referred to Karl-Heinz Rummenigge as the Bayern Munich chief executive. "He always knows that when there's an important occasion, he's going to be there and he showed it again tonight".
"I don't think there is a category for him", he said.
Ronaldo is Real's top scorer in La Liga this season with 19 goals.
For Alonso, this farewell was made all the more poignant because it was against Real, the club at which he spent five years of his career - playing his part in helping them reach the 2014 'La Decima'-clinching final in Lisbon.
A number of Bayern's players have since slammed Kassai for his display, with Vidal and Franck Ribery both posting pictures on Instagram of Ronaldo standing in a blatant offside position.
Their joint retirements signal the end of an era at Bayern, with time also running out for veteran wingers Franck Ribery, 34, and Arjen Robben, 33, who both have contracts until June 2018.
The Bavarians cancelled out their 2-1 quarter-final first- leg defeat to take the game to extra time in Madrid.
A Robert Lewandowski penalty and Sergio Ramos own goal, either side of Ronaldo's equaliser, sent the quarter-final into extra time.
This confirmation of Real Madrid's interest will surely have consecuences.