Rami Al Hajj marked his first Argyle start with a goal after eight minutes.
Substitute Ibrahim Cissoko scored twice in the second half, either side of Victor Moses' reply for the visitors.
Rooney said: 'I am delighted for the lads. Friday evening live on Sky and we had a lot of young lads in there, and I am delighted for them.
'It was a good performance for different reasons tonight, in the first half we controlled the tempo of the game.
Wayne Rooney hailed his Plymouth side after their impressive 3-1 victory over Luton on Friday
'Luton tried to press us and when we played with composure and through the press we caused them problems.
'Second half we were a little sloppy and gave the ball away a little bit too often but our back four were excellent.
'I thought how we dealt with (Elijah) Adebayo - who is a very difficult player to play against - was good and Luton are very good at set-pieces and I though how we defended against them was brilliant.
'We showed great character and desire to go and head the ball... and then the attacking players get all the praise because they score the goals.
'They were good goals as well. Rami, first start and great finish from him, and then Ibrahim came on and scored two, so all-in-all a good night.
'There were lots of things I was happy about. The conversation I had with the players in the week was the defenders will do a lot work to keep us in games and then the attackers get all the glory, which is exactly what happened tonight.
'What you are seeing is a real togetherness, everyone at the club - staff and the fans - everyone is buying into what we are trying to do. There's a really good feeling around the club.'
Luton boss Rob Edwards felt his side were outplayed in key areas of the pitch.
He said: 'Credit to the opposition. Both ends of the pitch they were better; they were more ruthless at one end and defended better at the other.
'I think we got into their final third 40 odd times, twice as often as they did but we didn't make their goalkeeper work enough.
'We weren't clinical enough at one end and then we didn't defend well enough at the other and that's not a good recipe to win a football match.
'They did those two things better than us and so they deserved to win the game.
'It was really frustrating to come away without anything, to lose at both ends of the pitch.
'We are trying. The lads are giving everything and trying to do the right things. I don't want to come out making excuses. I have given Plymouth credit. They were better than us at both ends.
'I am convinced we are going in the right direction and things will go our way soon.'