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Gareth Bale scored four for the first time in his Madrid career, whilst Karim Benzema struck his second hat-trick in three games as Real became the first side to score 10 in a La Liga match in 55 years.
However, as in recent matches at the Santiago Bernabeu, Benitez was booed before the start of the game and the calls for him to go grew when Real briefly trailed 2-1 early in the first-half before two Rayo red cards in the opening half hour swung the game in Madrid's favour.
"The fans weren't happy at certain moments of the game when we committed errors no one wants to see, but we solved the problems and knew how to react to the situation presented to us," said Benitez.
The former Liverpool and Chelsea boss has been publicly backed by president Florentino Perez despite rumours that he could be one defeat away from the sack after losing 1-0 at Villarreal last weekend.
And, after his most prolific day in his three-year Madrid career, Bale also offered his support to Benitez.
"We get on well and we continue to work and train hard," said the Welshman.
"We need to improve in every area, but we will get better as the season goes on."
Madrid captain Sergio Ramos is one of a number of key figures in the dressing room to have already clashed with Benitez, but he admitted the players have to accept whatever Perez decides.
"If the president says Benitez is the solution, that is what he will be," said Madrid captain Sergio Ramos.
"We are pawns, he (Perez) is the king."
Cristiano Ronaldo also scored twice to take his tally this season to 23, but could be seen asking the fans to get off the team's back when they fell behind.
And Ramos defended the World Player of the Year's right to tell the club's fans what he thinks.
"The fans are free to cheer or boo, but so are the players to express their views," he added.
"Cristiano is used to saying what he thinks. Today we were booed when the team most needed support. It wasn't there, but we have to remember the good thing which is the team knew how to react.
"It is a complicated situation because we aren't where we want to be. The fans are very demanding and they always want the team to win and play well.
"We have to stay calm, united and get the results to achieve our objectives."