Madrid were level two minutes after the break when Carvajal found space on the right and fired in a cross which Ronaldo volleyed past Neuer.
Nevertheless, the opener was scored at the other end of the pitch as Arturo Vidal headed home a corner kick from Thiago Alcantara to break the deadlock seven minutes later. "We would have preferred to have scored another goal", Real Madrid coach Zinedine Zidane told French TV. "Real have the better chance now but we still have a chance too, and we'll play with everything we've got".
"We played really well, we scored early [after half-time] and the game became easier".
But Ronaldo equalised nearly immediately following half-time by knocking home Dani Carvajal's cross, then provoked two bookings which saw Bayern centre-half Javi Martinez sent off, and completed the comeback by stabbing in a cross from substitute Marco Asensio.
Cristiano Ronaldo rounded on his critics after becoming the first man to score 100 European goals before after ending a six-game Champions League goal drought with a double against Bayern Munich yesterday.
Javi Martinez's sending-off just after the hour mark handed Real the initiative, and the 32-year-old Ronaldo clinched Real's victory when he beat Manuel Neuer after being picked out by Marco Asensio in the 77th minute. "With our second half, playing very well, keeping the ball from the opponent and the chances we had, it is clear that another goal would have been better".
Bale will therefore be sidelined in Gijon with a view towards being included for Tuesday's second leg against Bayern.
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Real defender Sergio Ramos had the ball in the Bayern net with time running out, but the goal was ruled offside but the Spaniards have the upper hand for the second leg at home next Tuesday.
Robert Lewandowski will be fit for the second leg of Bayern Munich's Champions League quarter-final against Real Madrid, according to Karl-Heinz Rummenigge.
"[Manuel] Neuer was good, he made a few saves". The second half is hard to judge.
"With patience we got the equaliser at the start of the second half, and from there it was another game".
Cristiano Ronaldo and Dani Carvajal are both just one yellow card away from a suspension and will be rested on Saturday to avoid the possibility of a ban that would see them miss the crucial Clasico clash at the Santiago Bernabeu next weekend.
"Gareth Bale felt a tweak at halftime and that I didn't need to take any threats", Zidane said.