Arsenal have won all of their matches when scoring first in the Europa League this season
Kieran Tierney's thumping 20-yard drive into the bottom right corner ensured the Gunners finished top of Group A on 15 points, two clear of PSV Eindhoven.
It was also the Premier League leaders' 10th victory in 12 matches in all competitions, a habit Arteta is keen to retain with his side facing three more matches until their season breaks for the World Cup in Qatar.
"Job done. I don't think it was the prettiest game we have played but we manage to win it," Arteta told BT Sport.
"Today was really important. We know how important it is going to be with all the teams playing in February. Winning helps winning.
"The atmosphere in the dressing room is much better after a win than a loss."
While Arsenal's margin of victory could have been more significant, there were still other positives for Arteta to take.
The Spaniard was able to introduce Bukayo Saka after the break to allay any fitness concerns and he also rested several key players prior to Sunday's Premier League trip to Chelsea.
The only complaint was that Arsenal did not put the result beyond doubt during a dominant first-half display in which Eddie Nketiah twice stung the palms of Zurich goalkeeper Yanick Brecher, and Fabio Vieira saw his goalbound effort blocked from close range.
That ensured a nervy finale with Adrian Guerrero's left-foot effort ruled out for offside and Ukrainian forward Bogdan Viunnyk seeing his rasping drive just fly wide of the top left corner as the visitors searched for an equaliser.
However, the hosts held on and have now won all eight of their matches against Swiss clubs in European competition.
Arsenal's defeat at PSV had left them needing a win to guarantee their progress without the prospect of a two-legged play-off in February against one of the clubs dropping down from the Champions League.
While they made a slow start, largely due to their improvised line-up containing seven changes from last Sunday's 5-0 win over Nottingham Forest, the Premier League leaders achieved their objective.
Arteta's side have now won all nine of their home games in all competitions this season but this performance will not be one he is likely to refer back to quickly, and he will also have been concerned to see Japan international Takehiro Tomiyasu limp off less than 15 minutes after coming on as a substitute.
And as nerves appeared to creep in with news that PSV were leading in Norway against Bodo/Glimt, Arsenal retreated towards their own goal providing plenty of encouragement to opponents currently languishing six points adrift at the bottom of the Swiss League.
The form of Gabriel Jesus, who has now gone eight games without a goal, is also a situation Arteta believes will alter with the Brazilian missing a glorious opportunity after the break as Brecher again came to the rescue for the visitors.
"It does bother him for sure," Arteta added.
"When he scores two he wants to score four. He had a couple of good chances but what he generates for the team is amazing. Last week he gave three assists. Today he was involved in every action again. The goals will come."
-- Courtesy of BBC Sport