It was far from a fluent display in the summer sunshine but Mikel Arteta’s side, once again regarded as the team most likely to halt Manchester City’s domination, deserved the points.
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 Ait-Nouri and Rodrigo Gomes both failing to trouble Arsenal keeper David Raya from promising positions when the score was 1-0.
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 — a 2-1 win ultimately in vain as City sealed a fourth successive crown.
The mood around The Emirates could not have been more relaxed this time in sultry north London — both on and off the pitch as Arsenal won without having to engage all their gears.
Wolves, handing debuts to new signings Jorgen Strand Larsen and Gomes, played the role of well-behaved guests, enjoying a fair share of the ball but threatening little.
Arsenal, runners-up to City for the past two seasons, dominated the opening period and took the lead when Saka was given too much time to pick out Havertz who directed his header into the corner to give keeper Jose Sa no chance.
Carelessness set in for Arsenal, however, and Wolves came closest to an equaliser when Hwang Hee-chan’s cross was met by Larsen with a header that Raya did well to keep out.
Arsenal laboured after the break but the points were secured when Saka, Arsenal’s top league scorer last season and most dangerous player on Saturday, cut in from the right and buried a left-foot shot past Sa.
“Saka is unbelievable. There are not a lot of players like him on the planet and he is still so young,” Havertz said.