"It's a big win for us and great to start the new year in such a positive fashion. We want to keep a gap between us and the other teams and make it as big as possible. If we keep winning our games, then it'll be very difficult for them to catch us up.
"It was very important to win and keep Chelsea eight points behind. We have to go on from here."
Van Bronckhorst is still easing himself back from a serious knee injury and was delighted to score his first goal since a 3-1 win at Leicester last January.
Wenger has been using the 27-year-old in rotation, but the Dutchman is determined to make himself a first-team regular.
He said: "I was thrilled to score and lots of things raced through my mind.
"I was thinking about all the hard times I had last year, so to be playing again and scoring in a game like this is a great achievement. It makes all the hard work worthwhile and means a lot.
"My aim now is to get a regular place in the team."
