Benzema double helps France ease past Armenia
The win followed a 1-0 victory over Portugal and a 2-1 success against Serbia in September.
Benzema was on target in the 77th and 79th minutes after Antoine Griezmann (35) and Yohan Cabaye (55) had put the French firmly in the driving seat.
The win also set up Didier Deschamps's side for stronger future challenges with friendlies against Denmark, world champions Germany and England to follow before the end of the year.
Griezmann hit his sixth international goal in his 21st game after being teed-up by Benzema, who enjoyed a much-needed confidence-boosting evening.
The Real Madrid star is top of the scoring charts in Spain but had not netted for France since October 2014.
But before the end of the night, he had tucked away his 26th and 27th international goals in his 81st outing.