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Xabi Alonso's team, who have now gone a league-record 29 matches without defeat this season to secure their first trophy since 1993, have a 16-point lead over Bayern with five matches remaining.
Bundesliga leaders Bayer Leverkusen secured a last-gasp 2-0 home win over West Ham United.
Federico Valverde salvaged a draw for Real late on after City had taken a 3-2 lead with sumptuous strikes from Phil Foden and Josko Gvardiol following a Ruben Dias own goal and Rodrygo strike that gave the hosts a half-time lead in Spain's capital.
Paris St Germain, who are seeking their first Champions League title, will take on Barcelona while Atletico Madrid face Bundesliga side Borussia Dortmund, which means all three Spanish teams have the opportunity to reach the semifinals.
Paris St Germain's Kylian Mbappe scored twice to lead them into the Champions League quarterfinals.
Bayern CEO Jan-Christian Dreesen said there would a 'a new direction' next season with a new coach.
The attacking full-back and dead-ball specialist became an instant Germany football great when his spot-kick earned them a 1-0 victory over Diego Maradona's Argentina in the World Cup final in Rome in 1990.
Disciplined Lazio stifled the German side's attacks and Bayern were toothless throughout, failing to get a single effort on target in the match.
The event drew 30,000 fans who celebrated the return of the 36-year-old midfielder, who joined the club last month.
Beckenbauer won the World Cup with Germany in 1974.