Lucky game for Arsenal you say, I can't say the same because this is a well deserved result, Arsenal obviously was the best team of the night, they controlled the entire game, there was no way Chelsea were coming back into the game. If not for a minute of carelessness, Chelsea wouldn't have gotten a goal even. The win wasn't a lucky one in any way.
obviously it wasn't luck that Arsenal got, all because Arsenal's performance is stronger than Chelsea and Chelsea is indeed not a draw opponent for Arsenal.
and no matter how good Arsenal are, they still cannot beat the performance of Man City players, who are far better than Arsenal. we can see that Man City was previously far behind Arsenal but can catch up to Arsenal's points and I think in the next game I think Man City will take Arsenal's position again.
Arsenal were sloppy and gave Chelsea a goal, I think it has become a routine for Arsenal to concede at least a goal even in games they have full domination and last night was no exception, they lost focus as usual and gave Chelsea a good chance and Noni Madueke was smart enough to capitalize on the opportunity to get his first EPL goal for Chelsea.