Holders Real Madrid survived a huge scare when they lost 4-3 to Schalke 04 in the Champions League on Tuesday but squeezed into the quarter-finals 5-4 on aggregate thanks to record European marksman Cristiano Ronaldo.

Coming hard on the heels of a 1-0 defeat at Athletic Bilbao in La Liga last weekend, the loss to a battling Schalke side did nothing to dispel the impression Real have lost their way and they were whistled off the Bernabeu pitch by their angry fans.

Two first-half goals from Ronaldo, which took his tally in European competition to a record 78 goals, and a Karim Benzema strike just after the break saw Real reach the last eight but Schalke came close to pulling off a remarkable comeback.

Striker Klaas-Jan Huntelaar scored twice for the visitors, including a superb late winner on the night, after Christian Fuchs has put the German side in front after 20 minutes, with substitute Leroy Sane also on target for the Bundesliga side.

Video credit: VTV

It was Real's first Champions League defeat at home in 22 games since Barcelona beat them 2-0 in April 2011 and was only the second time the world's richest club by income had conceded four goals in a European game at the Bernabeu.

"We didn't play well but sometimes you have to suffer," Real midfielder Luka Modric, returning to action as a second-half substitute after along-term injury absence, said in an interview with Spanish television.

"We have to play as a team and hopefully we will get back to playing the way we did at the start of the season," added the Croatia international, who had been sidelined since November.

"We have the quality and I think we will see the best version of Real Madrid in the next match."

Deserved lead

After Real comfortably won last month's last 16, first leg in Gelsenkirchen 2-0, Schalke came out fighting and took a deserved lead when Fuchs' shot ricocheted into the net off Real goalkeeper Iker Casillas.

Ronaldo levelled from a Toni Kroos corner five minutes later before former Real striker Huntelaar, who moments earlier had struck a fierce shot against the crossbar, put Schalke 2-1 ahead when he followed up Max Meyer's saved effort.

Ronaldo struck again from Fabio Coentrao's cross on the stroke of halftime -- the Portugal captain's 75th Champions League goal putting him level at the top of the all-time scoring chart with Barcelona forward Lionel Messi.

Both sides continued to attack at every opportunity in the second half and Benzema made it 3-2 in the 53rd minute before Sane curled a shot past Casillas in the 57th to equalise.

Dutchman Huntelaar set up a nervous finish when he smashed a brilliant effort into the net off the bar six minutes from time and Schalke captain Benedikt Hoewedes had one more chance to snatch the decisive goal but a relieved Real held out to claim a place in the draw for the last eight on March 20.

Real outplayed

Real were looking for a convincing performance after the defeat at Bilbao cost them top spot in La Liga but they were outplayed for long periods by an impressive Schalke unit.

Both sides were pushing forward in search of goals, which made for an entertaining spectacle but allowed the visitors plenty of chances to counter attack.

Benzema's goal, when he picked up a loose ball and darted across the penalty area before firing into an empty net, seemed to have settled the tie but Sane's brilliant leveller at 3-3 gave Schalke renewed hope.

Schalke midfielder Tranquillo Barnetta came close in the 62nd minute and Real fullback Alvaro Arbeloa burst through in the 65th but was denied by a fine save from Timon Wellenreuther.

Ronaldo's brace took his goals tally past Barcelona's Lionel Messi (76) and former Real striker Raul (77) in European games.

He also matched Messi's record of 20 Champions League doubles and took his total for the season to 41 goals in 38 appearances in all competitions, also level with Messi.

Real's defeat meant they missed a chance to set a record for consecutive victories in Europe's elite club competition.

They equalled the mark of 10 straight wins set by Bayern Munich in 2013 when they beat Schalke in the first leg.