Benzema ended a three-match scoreless streak when he tucked in from close range four minutes into Sunday's 4-2 La Liga victory, before doubling his tally with a slick first-time finish on the stroke of half-time.
He also played a crucial role in Madrid's fourth, dribbling his way in from the flank before combining with Lucas Vazquez to tee up substitute Gareth Bale on his return from injury, and was unfortunate not to claim an assist when Dani Carvajal struck wide moments later.
And Solari was quick to praise the 31-year-old Frenchman, who now has nine Liga goals to his name this season.
"He always makes complete performances, but he has also scored two beautiful goals," Solari told a news conference. "We totally trust in him and he is demonstrating all of his quality more than ever all this season."
Benzema's Madrid team-mate Vazquez echoed Solari's thoughts, adding that the Frenchman has to be considered as the world's most complete centre forward.
"I think Benzema has proved to us all that he's the best number nine in the world," Vazquez told reporters. "Working hard for the team, combining with his team-mates, he's wonderful."
Bale's goal – a venomous strike following a clever turn – ultimately proved decisive for Madrid, with Raphael Varane's red card handing Espanyol hope before Roberto Rosales volleyed home to make it 4-2.
The former Tottenham forward has endured another injury-hit campaign, but Solari is confident that Bale will recapture his best form soon enough.
It’s great to be back! +3 pic.twitter.com/9LT9H7hYdi— Gareth Bale (@GarethBale11) January 27, 2019
"Gareth is a decisive player, he’s always capable of scoring a goal. He scored as soon as he came on and that was good for the game and his confidence," Solari told Real Madrid's official TV channel.
"Step by step he has to regain the form from before the Club World Cup when he scored three goals.
"This is the Gareth we want to see all the time, like today when he was hungry to score."