Jose Mourinho's side finally rid themselves of a six-year Champions League curse when they dismissed Olympique Lyon 3-0 on Wednesday to progress to the quarter-finals of Europe's elite club competition for the first time since 2004.
They have 10 matches left to catch Barca - who host Getafe earlier on Saturday and have 75 points from 28 matches to Real's 70 - and prevent their great rivals from securing a third straight La Liga title.
The two clubs are due to meet in next month's King's Cup final, only days after they clash in Spain's "Clasico" in Madrid, and could be picked to play each other home and away when the Champions League draw is made on Friday.
"We are very happy with the win," defender Marcelo, who scored the opening goal against Lyon at the Bernabeu on Wednesday, told reporters.
"It was a very important victory for everyone, the team and the fans, after some difficult seasons," the Brazilian added.
"We had a debt to the Madrid family and thank God we were able to get through. That makes us more relaxed."
Real look to have a significantly tougher run-in to the end of the season, with away games at Atletico, Athletic Bilbao, Valencia, Sevilla and Villarreal as well as next month's game at home to Barca.
The champions travel to Villarreal early next month but the only other top-eight team they are still to play, apart from Real, are local rivals Espanyol, whom they meet at home on the second weekend of May.
BIG BLOW
Real have history on their side for Saturday's clash across town at Atletico's Calderon stadium, having not lost to their city rivals since a 3-1 defeat at the Bernabeu in October 1999.
Atletico striker Diego Forlan believes the club's woeful run against Real is there to be broken.
"There are no favourites and anything can happen on the pitch," the Uruguay striker, who has had a patchy season after sparkling at the 2010 World Cup, said at a news conference on Wednesday.
"We have the team to play a good match, a complete match, and to be at a high level," the former Manchester United and Villarreal player added.
"We cannot afford to make mistakes in defence and in attack we must be very precise."
Barca's preparations for the Getafe game have been overshadowed by the news this week that defender Eric Abidal needs surgery on a liver tumour.
The France international, who has been on imperious form this term, is due to go under the knife on Thursday and it is unclear how long he will be sidelined.
"It's a big blow for him and for the team," former Barca player and coach Carles Rexach said on the club's website.
"When you see something like that happening to someone close you realise that the most important thing is your health."
