Real Madrid looked slow and disjointed at Vallecas and were almost held to a goalless draw until Benzema and Vinicius Junior worked their magic seven minutes from time.
The France striker found Vinicius with a brilliant through pass and ran into space to receive the ball back and finish from close range with a single touch.
LaLiga top scorer Benzema and Vinicius have now scored 32 of the team's 52 goals this season between them.
After the match, Real manager Carlo Ancelotti said: "I'm very satisfied with the effort, the commitment, the intensity of the team. We won. It was difficult with the atmosphere, the opponent, the pitch, it was complicated so I think we did well, not many teams have won here. It was a game that had to be like that, and we delivered."
"It was a complicated game mostly due to the field being in very poor condition," Courtois told reporters referring to the pitch were large sections were threadbare.
"I don't think it's good for LaLiga's image to play in a field like this. It's far from ideal. Good for us that Benzema and Vinicius are in-form. After four years together they reached a level of connection that is incredible."
Rayo players were also far from happy when referee Isidro Diaz de Mera failed to send off midfielder Casemiro despite a studs-up challenge on Oscar Valentin. The incident was reviewed but VAR allowed the yellow card shown by the referee to stand.
Ancelotti was also asked about his midfield trio for Madrid's Champions League second leg against Paris Saint-Germain on March 9 and hinted Luka Modric, Toni Kroos and Federico Valverde could be picked there.
"It could be yes, it's the midfield that has the most chances of playing that game," said Ancelotti, whose team trails PSG 1-0 on aggregate after the round-of-16 first leg. "I have to say that Valverde came on and played well, Rodrygo too, they brought energy to the team at an important moment in the game."