Benzema, 22, had previously managed just three goals in all competitions this season and was behind Gonzalo Higuain in the pecking order under new coach Jose Mourinho.
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Auxerre's efforts were in any case in vain as Ajax Amsterdam's 2-0 victory at AC Milan secured third position in Group G for the Dutch side and a spot in the Europa League.
Ronaldo, one of three regular first-teamers in the suspended Mourinho's starting 11, crossed for Benzema to nod in the opening goal in the 12th minute.
The Portugal winger lashed home the second in the 49th after Marcelo's fine through ball sent him clear and Benzema netted in the 72nd with a low shot.
"I am very pleased to have scored three goals," Benzema told Spanish television. "I am feeling better every day and that is being reflected on the pitch.
"I am going to work hard to play like I have done today all the time."
Real are looking to end a poor run in Europe's elite club competition during which they have failed to make the quarter-finals the past six seasons despite investing heavily in players and coaching staff.
Benzema's opening goal was the club's 300th since the Champions League was created in 1992/93, the first side to reach that total.
"I said before that Real have what it takes to win the competition and I would say that they are one of the favourites," said Fernandez.
"Our priority now is to play a good (French) league campaign and secure our place in the first division," he added of the 13th-placed team.
Real's reserve goalkeeper Jerzy Dudek had a mixed night, making two excellent saves to deny Jean-Pascal Mignot and Dennis Oliech in the first half before going off after getting a bang on the head in a collision with Roy Contout.
