Wenger delighted with "dangerous, fluent" Arsenal
While Adebayor's contribution was vital, Wenger praised Theo Walcott for the way he responded after a superb treble for England in midweek.
Wenger said: "We looked dangerous and fluent going forward. It was a well-accomplished victory.
"You can be successful when you express your strengths and we did that today.
"Blackburn are dangerous going forward and I am happy we did not concede any goals.
"It is another big game on Wednesday and in the Champions League it is important to start well.
"We are in a tough group and Kiev are experienced as well as being a strong side at home.
"This victory, however, will give us confidence as we know we will have to put in a similar performance next week."
Walcott set up the opening goal for van Persie after eight minutes with a jinking run before Adebayor took centre stage.
Adebayor scored his first Premier League goal of the season before half-time with a free header, added a second from the penalty spot before completing a superb individual display in stoppage time.
Wenger admitted he had toyed with the idea of resting Walcott only to change his mind - and it paid off.
The 19-year-old came off after 63 minutes to a rousing reception from the visiting supporters.
Wenger said: "I assess every individual and I thought about leaving him out. But he gives us balance and penetration away from home.
"Theo can play on the right or the left. He likes both sides - he has been educated like that.
"The problem when you score three for the national team is everyone expects you to score three again in the next game.
"We know he can be dangerous but for me the most important thing is he has a team attitude. He works hard for the side and we will give him time to develop."