Benzema opened the scoring only four minutes into the match in Barcelona and also provided several smart passes for his teammates that went close to producing more goals.
In all competitions, Barcelona says the 31-year-old Messi has scored an astonishing 575 goals in 658 appearances.
Benzema has been key since Solari took over from the fired Julen Lopetegui two weeks ago and revamped Madrid.
At 1-1 in the 48th minute and with Leganes holding their own, Benzema skillfully headed in an out-swerving cross from Marco Asensio despite tussling with defender Jonathan Silva.
Benzema scored twice and Bale once as Madrid came from behind to earn a 4-1 win at Girona on Sunday, remaining perfect in the Spanish league after two rounds.
Tottenham manager Mauricio Pochettino and Germany coach Joachim Loew are two of the top names rumoured to be on Madrid's list of candidates.
Karim Benzema was a surprise addition to the starting lineup in the Champions League semifinal against Bayern Munich.
Real Madrid conceded early again at home and barely held on for a draw 2-2 against Bayern in Tuesday's semifinal match, advancing 4-3 on aggregate.
Ronaldo netted twice and his partners in attack added a goal each to record a fourth straight win for Real Madrid in the Spanish league.
Zidane started the strike trio of Ronaldo, Karim Benzema and Gareth Bale for the first time this season and the results were delivered.
The two forwards have not been in the best of terms when it comes to assisting each other but the Frenchman believes that the Portuguese's arrogance is good for the team.
Along with Gareth Bale and Cristiano Ronaldo, the French striker is a part of Madrid's "BBC" which has been a cornerstone of their success.
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