The London club swept aside 10-man Hull 4-1 with two goals from Alexis Sanchez capping a dominant display that might have eased the minds of some Arsenal fans underwhelmed by their start to the season.
They went into Saturday's Premier League match on the back of a fortunate 1-1 draw against Paris St Germain in the Champions League, days after they stole victory against Southampton with a penalty in the dying seconds.
The game with Hull, who had made a more positive start to the season than many had predicted, was far more straightforward and gave Wenger's men a third straight league victory for the first time since January.
"Overall we had a convincing performance in two different situations," Wenger told reporters.
"Eleven against 11, I thought we played well. When you play 11 against 10, it is of course not the same mentally and psychologically but we remained serious and in the end we won the game in a convincing way.
"We had a very difficult game against Southampton last week, went away to Paris St Germain. We go away again so you are happy with the three points."
Despite a mixed start to the campaign Wenger's side are third in the table, five points adrift of early pacesetters Manchester City.
There were impressive individual performances at Hull from the often-criticised Theo Walcott, 20-year-old striker Alex Iwobi and Sanchez who missed out on a hat-trick after failing to convert a first-half penalty.
Wenger said that Sanchez should not have been taking the penalty.
"Santi (Cazorla) was down to take it. I don't know why it did not happen, they have a pecking order," added the Frenchman.
"I want to know what happened and for it not to happen again. Overall anyone can miss a penalty, we have to accept that."
(Reporting by Toby Davis; Editing by Tony Jimenez)
