The lead lasted all of three minutes as Benzema headed a right-sided cross from Lucas Vazquez past Sergio Asenjo from eight yards and the turnaround was complete when Varane leapt highest to guide Toni Kroos's deep free-kick back across goal.
Luis Garcia's charges on the other side can to the game lying third from bottom on the table, fighting relegation midway through the La Liga campaign.
France World Cup-winner Varane made no mistake with a header of his own in the 20th minute, though, powering in from Toni Kroos' cross for his first club goal in nearly two years.
Solari explained after the match that Modric was not fully fit and it was always his plan to withdraw the Ballon d'Or victor.More news: German police: Man intentionally drove into crowd, injured 4
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It kept them in fourth place, seven behind leaders FC Barcelona after 17 games.
But Real Madrid could still have snatched a victor when substitute Isco burst into the area but was denied by Villarreal goalkeeper Sergio Asenjo.
"We head home angry because it was a game we wanted to win and we let it slip with a lapse in concentration", he said, as quoted by Madrid's official website. Gareth leaving like that cost us as he had a problem and we missed that counter-attacking edge, and Gareth is a specialist at just that.
"This result will give us strength", said Villarreal coach Garcia, who has taken two points from two games since succeeding the sacked Javi Calleja.
Villarreal have punched below their weight this season and in strikers Gerard Moreno who scored the only goal as his former club Espanyol beat Madrid a year ago, Carlos Bacca and Toko Ekambi, they have a mixture of height and pace able to cause problems to the Madrid defense.