Ander Herrera opened the scoring before Rooney fired an unstoppable effort past Brad Guzan following Angel di Maria’s cross.
Benteke pulled a quick goal back for Villa but Herrera sealed the three points for United with a finish late on.
Van Gaal hailed Rooney following the match and reserved particular praise for the United captain’s strike.
When asked about Rooney’s goal, van Gaal said: ”It was beautiful and also the assist of Di Maria. I think he was one minute on the pitch and he already has an assist. That’s fantastic.
“But after Wayne’s fantastic goal, the concentration went again. You saw that – at the kick-off we didn’t have pressure on the ball and then you know what can happen.
“We also know that Benteke is very dangerous in front of the goal because he can head and shoot, and he also scored against us in the away match. It was a stupid goal against us.”
Rooney had been criticised by some United fans following his largely anonymous display against Liverpool last time out so it was good to see him answer any doubts in resounding style.
The form of the 29-year-old will make it difficult for Robin van Persie to get back into the team following his return from injury. Van Gaal has spoken of how he does not want to change a winning team so it is unlikely he will drop Rooney or move him back into midfield.