There was a luck factor for Arsenal in their late victory against Manchester United. Arsenal didn't have many good chances to score although at the end of 3 out of 5 attempts their goal was enough to get them a full 3 points at home. Of course it's great, but I don't think I can beat Manchester City and Liverpool in the same way.
Before talking about luck, I would check the statistics first:
Shots - 17:10
Shots on target - 5:2
Corners - 12:3
Ball possession - 55% : 45%
I see that Arsenal dominated literally everything and I'm not surprised that this was reflected in the score. As for other opponents, there will be a different situation, and so far no one knows who will be stronger. If I were the manager of United, I would at least take care to confidently beat outsiders and average teams, this team is hardly capable of more.