Beginning their quest for a first Premier League title in 21 seasons, as well as attempting to extend their terrific streak of success against Wolves, Arsenal had two key attacking figures to thank for a somewhat nervy opening victory.
After Saka and Havertz combined for the latter to nod home Arsenal's first top-flight goal of the campaign in the first half, the same pairing swapped roles in the second for Saka to bag the critical insurance goal.
Havertz's opening header came when Arsenal were very much in the ascendancy, but by the time Saka wrapped up an opening three points for Arsenal, Mikel Arteta's men had started to seriously come under the cosh.
Gary O'Neil's Wolves offered very little threat in the opening 45, barring one terrific David Raya save from a Jorgen Strand Larsen header, but they asked questions of the Arsenal backline either side of the hour mark.
The West Midlands side forced their hosts into a couple of defensive mistakes, but failure to convert that pressure into anything meaningful proved their downfall in North London, as Arsenal won their opening game of a top-flight season for the third year running.
In contrast, Wolves have now suffered four opening-day losses on the spin for the first time in their Premier League history, but a record of the more desirable kind was set by Gunners defender William Saliba.
En route to another clean sheet, the Frenchman reached 50 wins for Arsenal in just 66 matches, breaking the previous record of 70 set by former left-back Nacho Monreal, another statistic for Prime Minister Keir Starmer - in attendance to watch his beloved Gooners - to smile about.
ARSENAL VS. WOLVES HIGHLIGHTS
25th min: Arsenal 1-0 Wolves (Kai Havertz)
Arsenal's patience pays off as Havertz nods in their first goal of the Premier League season. Oleksandr Zinchenko sprays a slick outside-of-the-foot pass to Saka out on the right, and the Englishman chips in a lovely inswinging cross.
The delivery is just too high for Thomas Partey, but Havertz leaps highest to hammer a bullet header into the Wolves net, which was unguarded as Jose Sa came out to punch Saka's cross clear and missed.
73rd min: Arsenal 2-0 Wolves (Bukayo Saka)
Breathing space for Arsenal just as Wolves were beginning to get a foothold on the game. Saka - who had picked up a needless booking earlier in the second half - goes from provider to goalscorer, while Havertz swaps roles too.
The German saunters forward against a backtracking Wolves backline and lays off Saka, who shifts the ball onto his favoured left foot inside the box and unleashes a vicious effort that flies past Sa at his near post.
MAN OF THE MATCH - BUKAYO SAKA
While David Raya earned his keep, there were only two real candidates for the Man of the Match accolade, and while Havertz took his header with aplomb before teeing up Saka, the England attacker just pips his German colleague to the prize.
The 22-year-old's delivery for Havertz's opener was simply sublime, and when everybody though that his second-half strike was bound for the far corner, he stunned the crowd and Sa with a clinical near-post finish.
Saka ended the game with five chances created in total, and while a needless yellow card was a slight blot on the notebook, he is up and running for the 2024-25 season in typically scintillating fashion.
ARSENAL VS. WOLVES MATCH STATS
Possession: Arsenal 53%-47% Wolves
Shots: Arsenal 18-9 Wolves
Shots on target: Arsenal 6-3 Wolves
Corners: Arsenal 8-2 Wolves
Fouls: Arsenal 17-14 Wolves
BEST STATS
WHAT NEXT?
In seven days' time, Arteta faces up to the man he succeeded in the Arsenal dugout in the Gunners' first away game of the season, which comes at fellow Champions League contenders Aston Villa in the 5.30pm kickoff.
Meanwhile, Wolves will have an additional day's rest before their first home match of the 2024-25 campaign, where they host Enzo Maresca's Chelsea on August 25.