Madrid and Barcelona are locked on 78 points at the top of the table, but Real have a game in hand over their title rivals.
Barca remain top thanks to their better head-to-head record as Lionel Messi struck twice to relegate Osasuna in a 7-1 thrashing.
Madrid boss Zinedine Zidane made nine changes in all from the side that lost 3-2 to Barca on Sunday to reignite the title race.
"It is the hardest job for a coach. When they play like they did today and then maybe they won't play in the next game," said Zidane.
"We know I have a phenomenal group of players and all of them are ready for the challenge between now and the end of the season."
Alvaro Morata smashed home at the near post to give the visitors the perfect start after less than a minute.
However, the European champions have now kept just one clean sheet in their last 15 games and their defence was breached once more when Florin Andone turned home Gael Kakuta's mishit shot 10 minutes before half-time.
Vazquez, though, restored Real's two-goal lead before half-time and Zidane's men could even have reached double figures in a dominant second period.
Morata unselfishly teed up Rodriguez for his second of the night before Isco sealed a stunning individual display by smashing home 13 minutes from time.
- Messi homage -
================
At the Camp Nou, Barca fans paid homage to Messi's brilliance against Real in scoring the winner and his 500th goal for the club with the last kick of the game in Sunday's El Clasico.
The five-time World Player of the Year responded by opening the scoring as he pounced on an error in the Osasuna defence to stroll through on goal and lift the ball over the advancing Salvatore Sirigu.
But the Portuguese had arguably his best night in a Barca shirt as he drilled home Ivan Rakitic's cross to make it 2-0 on the half hour.
"We had the chance to use a lot of players that have played fewer minutes," said Barca boss Luis Enrique.
"It is a game that boosts those individuals, the team as a whole and gives us hope for the end of the season."
Roberto Torres's free-kick briefly brought Osasuna back into the game three minutes into the second half.
Firstly, Gomes slotted home his second of the night after Gerard Pique's initial effort came back off the post.
Messi then curled in his 49th goal in 47 appearances this season from the edge of the area.
The Argentine instantly made way for 19-year-old Carles Alena to keep him fresh for Saturday's Catalan derby at Espanyol.
Paco Alcacer also grabbed a double for Barca's fifth and seventh.
And in between times Javier Mascherano bagged his first goal in 319 Barca appearances by blasting home from the penalty spot.
And Real Sociedad boosted their chances of qualifying for the Europa League with a 3-2 win at Valencia.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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