While the midtable Bundesliga club thrashed Inter 5-2, Madrid take advantage of a 10-man Tottenham to win 4-0 in the first leg of their quarter-finals.
Schalke, Real all but in the semi-finals of Champions League with big wins
Schalke, which is struggling in midtable in the German league, thrashed reigning champion Inter Milan 5-2 away, with Raul Gonzalez scoring one of the visitors' goals to extend his competition-leading tally to 70.
Madrid took full advantage of a red card for Tottenham Hotspur striker Peter Crouch in the 15th minute to ease past the English side 4-0, with goals by wingers Angel Di Maria and Cristiano Ronaldo adding to Emmanuel Adebayor's double.
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"For a team with 10 men for such a long time, it's an impossible mission," Madrid coach Jose Mourinho said. "But with the English concept of football, it's not over."
The second legs take place on April 13 but both series already look to be over. Manchester United visit Chelsea and Barcelona host Shakhtar Donetsk in their quarter-final first-leg games later tonight.
Inter, looking to become the first team in Champions League history to retain the title, took the lead after just 29 seconds through a remarkable volley by Dejan Stankovic, who smashed a stunning effort into an empty net from 50 meters after Schalke goalkeeper Manuel Neuer raced out of his area to head the ball clear.
The holders later went ahead for the second time with Argentina striker Diego Milito's close-range finish in the 34th, but their deficiencies at the back were laid bare by Schalke after that. Inter, which was without suspended center back Lucio, wasn't helped by the red card shown to Romania center back Cristian Chivu for a second bookable offence in the 62nd — when the score was 4-2.
"We started well, but then it all went wrong in the second half," Inter captain Javier Zanetti said.
Joel Matip grabbed Schalke's first equaliser, in the 17th minute, before Edu scored the first of his two goals in the 40th.
Prolific former Real Madrid and Spain striker Raul put the visitors ahead for the first time in the 53rd, before an own goal by Andrea Ranocchia and Edu's second goal of the night sealed an emphatic win and set up a potential semifinal against Chelsea or United.
"It was a great night for us as not everyone scores five goals against the defending champion," Raul said. "After a difficult start, my team showed its superiority."
Mourinho stayed on course to become the first coach to win the Champions League with three different clubs as Madrid scored three second-half goals to sweep aside an increasingly jaded Spurs.
"It's one of those days where everything that could have gone wrong, did go wrong," said Tottenham manager Harry Redknapp, who lost right winger Aaron Lennon to illness a minute before kickoff.
"It's difficult to come here with 11 men, let alone to come and play with 10."
Former Arsenal striker Adebayor took his tally to 10 goals in 10 games against Spurs by opening the scoring in the fourth minute and adding the second in the 57th, both goals coming from headers from 10 meters out.
By that time, Crouch had been sent off for two reckless and very avoidable tackles in the space of seven minutes and although Spurs — playing in their first Champions League campaign — battled well in the first half, the floodgates opened after the break.
Di Maria cut in from right flank and bent a shot into the far corner in the 72nd before Ronaldo, who started after recovering from a hamstring injury, notched his 38th of the season with a volley that Spurs goalkeeper Heurelho Gomes fumbled into his own net.
The only negative on the night for Madrid was the yellow card shown to Pepe for a foul on Gareth Bale in the 36th, ruling the Portugal center back out of the return leg at White Hart Lane.
If the nine-time competition winners complete the job next week, they could face Spanish rival Barcelona in the semi-finals.