Havertz was a Champions League final hero for Chelsea in 2021, but he has endured a torrid time since crossing London to join Arsenal in the close-season.
The 24-year-old midfielder finally gave a glimpse of why Arteta splashed out £65 million ($80 million) to sign him when he headed home in the closing minutes.
Havertz's second goal for Arsenal was his first in his last 10 appearances, moving his team one point clear of second placed Manchester City, who were held to a 1-1 draw by third placed Liverpool earlier in the day.
"That is the beautiful thing about life. When you have challenges and you have to overcome them, it makes these moments much better," Arteta said.
"That is the reason the people reacted to him like that today. It is because he is adorable and he is a joy to work with. He fully deserves more than anybody to get that win."
Arsenal's third successive win in all competitions proved they have erased the bitter taste of their controversial VAR-aided defeat at Newcastle earlier in November.
Arteta's men had already won at the Gtech Community Stadium in the League Cup in September and they left it late before making it another successful trip to west London.
"I love winning and we are top of the table. This is where we have to want to be," Arteta said.
"When you have an opportunity to take a bite out of everybody you have to do it.
"I was really curious how the team was going to do. Winter has started, it was very cold and it is difficult coming to Brentford. I loved the way the team competed."
With on-loan Arsenal keeper David Raya not eligible to play against his parent club, Aaron Ramsdale made his first league start since September 3.
Ramsdale's father recently criticised Arteta's handling of the Arsenal goalkeeping controversy, with the England international surprisingly losing his place to Raya despite recording the second most Premier League clean-sheets last season.
But Arteta's faith in Raya received a boost when Ramsdale, his confidence clearly affected by his spell on the bench, almost gifted Brentford the lead with a horrendous mistake early in the first half.
Trying to play out from the six-yard box after Gabriel's back-pass, Ramsdale panicked under pressure from Yoane Wissa.
Havertz has the last word
Ramsdale missed his kick and the ball rolled to Bryan Mbeumo, whose shot was cleared off the line by Declan Rice before Wissa stabbed the rebound wide.
Arteta refused to be drawn on Ramsdale's shaky performance, saying only: "I am really happy with the team and the way the team played and we kept the clean sheet."
After a slow start from Arsenal, they finally showed signs of life when Trossard headed Oleksandr Zinchenko's cross over before Gabriel nodded into the side-netting.
Arsenal thought they had taken the lead in the 42nd minute when Gabriel Jesus met Bukayo Saka's cross with a header that was parried by Mark Flekken and Leandro Trossard nodded home from close-range.
But a VAR check decided Trossard was narrowly offside, giving Arteta another dose of frustration at the hands of the review system.
Brentford nearly made Arsenal pay for their lethargy as Neal Maupay's header was brilliantly cleared off the line by the stretching Zinchenko before the French forward poked the rebound wastefully wide.
That proved a crucial moment as Havertz came off the bench to win it in the 89th minute.
Saka's cross picked out Havertz's run to the far post and the German guided his header past Flekken as Arteta jumped for joy on the touchline.
