The Spanish giants are undoubtedly the competition’s most successful team, winning it a record 13 times – with Benzema lifting four of those titles.
The 33-year-old’s double, either side of Pedro Fernando’s equaliser, kept Real three points clear at the top of Group D.
Inter Milan moved above Sheriff Tiraspol into second place after a 3-1 win in Moldova Second-half goals from Marcelo Brozovic, Milan Skriniar and Alexis Sanchez preceeded a late consolation from Adama Traore.
AC Milan earned their first point with a 1-1 draw against Porto at the San Siro. Luis Diaz gave the visitors an early lead but they were unable to repeat their victory in Portugal a fortnight ago as Chancel Mbemba’s own goal meant it finished all square.
The result leaves the seven-time European champions on the brink of elimination.
Liverpool have run away with Group B and booked their place in the knockout stages with two matches to spare after a comfortable 2-0 win over 10-man Atletico Madrid.
This time there was no conceding of a two-goal lead as there had been in Madrid and at home to Brighton on Saturday after Diogo Jota and Sadio Mane’s first-half goals set up victory.
A somewhat harsh red card for Atleti defender Felipe for a challenge on Mane aided the cause as Jurgen Klopp’s side made it four successive group wins for the first time.
Manchester City struck three times in the second half to move closer to the last 16 with a 4-1 win over Club Brugge.
Phil Foden gave Pep Guardiola’s side an early lead in the Group A clash at the Etihad Stadium but a freak own goal from John Stones threatened to give the hosts an awkward night.
A draw might have damaged qualification hopes with a tricky clash against Paris St Germain still to come but goals from Riyad Mahrez, Raheem Sterling and Gabriel Jesus eased nerves.
The result meant City, who reached the final last year, now only need a point from their last two group games to return to the knockout stages.
That is because the other game in the group between RB Leipzig and Paris Saint Germain finished 2-2.
Dominik Szoboszlai held his nerve to net an injury-time penalty and get a first point of the board for the Bundesliga club, who had led early on through Christopher Nkunku’s header.
Georginio Wijnaldum’s double before half-time turned the game on its head but PSG were denied passage through on the night by Szoboszlai’s leveller.
Ajax are through after they made it four wins from four matches in Group C at Borussia Dortmund.
The hosts overcame Mats Hummels’ red card by taking the lead from the penalty spot through Marco Reus. However, Ajax really made their numerical advantage count in the second half with goals from Dusan Tadic, Sebastien Haller and substitute Davy Klaassen for a 3-1 success.
Sporting Lisbon put themselves firmly in contention for second place with a 4-0 home victory against Besiktas. Pedro Goncalves scored twice, the first from the penalty spot, while Paulinho and Pablo Sarabia were also on the scoresheet.