Xavi Hernandez's side leapfrogged Girona to move on to 76 points, one clear of their Catalan rivals who dropped points in Friday's 2-2 draw at Alaves.
If anything defines Real Madrid it is a relentless hunger for silverware and that remained clear even as they celebrated their 36th La Liga title triumph on Sunday.
Real Madrid claimed a record-extending 36th LaLiga title on Saturday after Girona's 4-2 thrashing of local rivals Barcelona left Carlo Ancelotti's side with an unassailable lead in the standings.
"We will keep fighting and next season we have to change a huge amount of things," said Xavi.
The club, in La Liga for only the fourth season in their history, beat Barcelona 4-2 at their tiny Montilivi stadium to secure a top four finish.
Carlo Ancelotti's side romped clear of last season's winners and shock challengers Girona to clinch their record-extending 36th La Liga trophy
Real Madrid, who have lost only once in the league this season, hold a 13-point advantage over second-placed Girona while Barcelona dropped to third
Real Madrid earned a comfortable 3-0 win over Cadiz which ensures they will win La Liga if Barcelona fail to beat Girona later Saturday.
Barcelona will be favourites when they visit Girona on Saturday but the hosts are ready to seize a historic opportunity to beat them in front of their own fans, Girona manager Michel said on Friday.
Nigeria forward Osimhen rolled home the leveller with 15 minutes left of the first leg of their Champions League last 16 tie at the Stadio Diego Armando Maradona, in his first match since returning from the Africa Cup of Nations.
Robert Lewandowski's brace snatched champions Barcelona a 2-1 win over lowly Celta Vigo to leave them third in La Liga, trailing leaders Real Madrid by seven points.
Barcelona have little room for error if they are to defend their LaLiga title, manager Xavi Hernandez said on Friday ahead of his side's trip to Celta Vigo.
Xavi Hernandez's side, third, shared the spoils with their relegation-battling opponents, 19th, after a thrilling battle at the Olympic Stadium, but now trail leaders Real Madrid by 10 points.
Barcelona coach Xavi Hernandez said Saturday goalkeeper Marc-Andre ter Stegen and winger Raphinha are fit again after injury to help the team's ailing title defence.
Barcelona Sporting Director Deco said that they are not looking to sign French forward Kylian Mbappe as it would only make the Spanish club “worse”.
Real Madrid coach Carlo Ancelotti said Saturday Barcelona complaints over his club allegedly influencing La Liga referees were unprofessional.
Barcelona earned a 3-1 win at Alaves in La Liga on Saturday with Brazilian teenager Vitor Roque scoring and then sent off in a lively appearance off the bench.
Barcelona president Joan Laporta said Friday that a European Super League project could begin as soon as next season, adding that he does not care if English clubs join or not.
Barcelona coach Xavi Hernandez complained Friday rivals Real Madrid are influencing referees "every week" and said it meant La Liga was "completely adulterated".