The Real Madrid striker clinically half-volleyed home Blaise Matuidi's pass in the 32nd minute before the Paris St Germain midfielder hooked home his first international goal nine minutes later to earn Les Bleus a 2-0 win.
The well-taken goal was Benzema's seventh in six games for club and country - a far cry from last season, when he went 16 months without an international goal.
His luck turned in October's 6-0 friendly win over Australia and he also scored in France's final Group I qualifier against Finland and in the dramatic play-off win over Ukraine.
Benzema told L'Equipe: "Blaise put the ball into my path, I knew where the goal was, I hit it and had a bit of success.A few months ago, it might have gone over the bar. Right now, I feel good in myself and that shows on the pitch. That has to continue."
Coach Didier Deschamps said: "We started the match a bit timidly but we injected some pace and rhythm which allowed us to take the lead.
"We were strong at the break. In the second half, we were more in control."
Deschamps reserved particular praise for Porto defender Eliaquim Mangala, a reported transfer target for teams including Manchester rivals City and United, who deputised for Laurent Koscielny and dealt well with Red Devils striker Robin van Persie.
"In Uruguay he made a mistake against (Liverpool's Luis) Suarez," said the coach. "Here it went better even though he had Van Persie up against him.
"It is not a surprise to me, even though he owed his selection to (Laurent) Koscielny's muscle problem.
"I was not worried, Eliaquim plays for a big club in Portugal and he plays in the Champions League. He is one of the players I think has good potential to be an international."
Deschamps handed debuts to Real Sociedad playmaker Antoine Griezmann on the right wing and Paris St Germain left-back Lucas Digne as a half-time substitute.
Griezmann said: "Before the match, the coach told me to play with freedom and not overthink things. He gave me a lot of confidence by putting me in the XI and I tried to repay him.
"I know my potential, I can play much better. It took me 10 or 15 minutes to get into the game, but after that it got better and better. If I have the chance to return, I will give even more."
Digne added: "It represents a step in a career and I had all my family there to live it with me. It was very special, very emotional, and it was great to start with a victory."
Netherlands coach Louis van Gaal admitted his side, who could have fallen even further behind had Raphael Varane not missed a glorious chance, had come up short.
"They did their best but we needed to be better at the end of the first half," he told De Telegraaf. "We did better after the break.
"At the World Cup we will have to take more risks to make good a deficit."