Cristiano Ronaldo netted his 100th European goal on Wednesday, scoring both goals in Real's 2-1 comeback win at Bayern.
Ronaldo netted his 100th European goal on Wednesday, scoring both goals in Real's 2-1 comeback win at Bayern, who had Javi Martinez sent off.
The Bavarians now have it all to do for the return in Madrid next Tuesday.
Bayern should have been 2-0 up at the break in Wednesday's first-leg, but Arturo Vidal, who headed the hosts into a first-half lead, skied a penalty.
The first-leg turned after the break as Ronaldo equalised, then Real dominated Bayern with the numerical advantage and peppered the Bayern goal.
Real deserved the win which Ronaldo sealed by reaching the 100-goal milestone on 77 minutes.
It could have been a higher score and Real captain Sergio Ramos had the ball in the net late on, but the goal was disallowed.
Ancelotti says the Germans still have a fighting chance in Madrid.
"We don't have a big chance, but it's still a chance -- we're still alive," said Ancelotti.
"They could have killed it (the tie) by scoring another goal, but they didn't.
"We had the game under control in the first-half, but we lost our efficiency after the break.
"It made life hard when we went behind, but we still have a chance."
Bayern have won only three of their 11 European matches at the Bernabeu -- the last of which was on penalties in 2011/12 after it finished 3-3 on aggregate.
Germany striker Thomas Mueller says the Bavarians have the necessary belief.
"We don't need a footballing miracle. The belief is still strong, or we wouldn't be FC Bayern Munich," he said.
"In my opinion, we didn't have the 100 percent conviction that we are the better team."
Winger Arjen Robben says the Bavarians will have to raise their game having been outplayed in the second half.
"We have to find the ten to fifteen percent in Madrid that we lacked this time," demanded Robben.
"We gave them too much respect and had too little bite.
"You have to pick your chin up, put the extra percent on it, and put in an outstanding performance in Madrid."
Ancelotti hopes to have striker Robert Lewandowski, who missed the first leg with a bruised shoulder, and defender Mats Hummels, ankle, back for the return.
"We have six days, we hope they will both be back," said the Italian.
Germany goalkeeper Manuel Neuer kept Bayern in the tie with a string of saves and believes his team can book a sixth straight semi-finals berth.
"It's important to finish the game with 11 men," said Neuer, on his first game back after foot surgery.
"We didn't have so much possession and we were missing our usual self-assurance.
"It could have finished much higher, but we believe we can still do it.
"We were the best team in the second half and it could have been two or three nil up."