The Gunners outclassed their hosts to win 4-0 and move to within striking distance of Manchester City – who visit the Emirates Stadium next weekend – but a late injury to Bukayo Saka will worry Arteta.
Havertz has struggled to make an impact since moving across London from Chelsea in the summer but stroked home a second-half penalty, much to the joy of his team-mates and the travelling support inside the Vitality Stadium.
Arsenal were already two goals to the good at that point, Saka breaking the deadlock with his fifth of the season, before Martin Odegaard scored from the spot with a Ben White header wrapping up the win in stoppage time.
Arteta was able to call on a number of players who were injury doubts ahead of the trip to the south coast as William Saliba, Declan Rice and Saka all started despite missing the majority of training leading into the game.
Saka, though, hobbled off for the second game in succession having injured a foot against Tottenham in last weekend’s north London derby draw.
Bournemouth are still without a league win under head coach Andoni Iraola, who very much came off second best in the battle against childhood friend Arteta.
Arsenal were on the front foot from the off as Havertz saw a shot deflected behind off Illia Zabarnyi and behind for a corner.
Saka duly put them ahead soon after, nodding into an empty goal after Gabriel Jesus’ header came back off the post and into the path of the England winger.
Oleksandr Zinchenko stung the palms of Neto with the visitors in search of a second goal, which arrived from the penalty spot after Max Aarons felled Eddie Nketiah.
Saka initially stepped up, only to give the ball to his captain with Odegaard dispatching the spot-kick to widen the gap before the break.
Bournemouth continued to cause their own problems as a poor challenge from Ryan Christie on Odegaard led to Michael Salisbury pointing to the spot for a second time.
Saka, again, collected the ball but this time ceded responsibility to Havertz, without a goal or assist in his first nine Arsenal appearances.
He coolly slotted home before being mobbed by his team-mates as his name rang out from the away section with the points all-but secured.
The only sour note of the afternoon for Arsenal came when Saka hit the deck in pain after a coming together with Milos Kerkez.
He limped on for a couple of minutes before being replaced by Fabio Vieira with Arsenal adding another goal late on through White.
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