Havertz headed in from Saka's cross in the 25th minute, but the hosts never looked completely comfortable until Saka's clinical finish doubled their advantage in the closing stages.
Wolves had their chances, with Rayan Aït-Nouri and Rodrigo Gomes both failing to trouble Arsenal keeper David Raya from promising positions when the score was still 1-0.
"I am really happy. With the first game, you have some uncertainty in how you will respond," Arteta said.
"We had our moment after 1-0 when we were not in control, but after Saka's goal we were much more comfortable. The way the boys go their job is unbelievable, so very happy."
Three months have passed since Arsenal fell just short of their first English title for 20 years on a nerve-jangling final day of the season at home to Everton.
The mood around the Emirates could not have been more relaxed this time in sultry north London -- on and off the pitch -- as Arsenal won without having to engage all their gears.
