The season's curtain raiser looked to be going the way of the Premier League champions when Cole Palmer gave them a 77th minute lead but substitute Leandro Trossard equalised deep into stoppage time to force penalties before the Gunners won the shootout.
Havertz was chosen to lead the line for Arsenal in the absence of the injured Gabriel Jesus and he caused the the City backline all sorts of problems in his 87 minutes on the pitch.
Havertz joined Arsenal from London rivals Chelsea for £65m earlier this summer.
“He was superb,” Arteta said after the win.
“The way he pressed and how intelligent he is to try and understand certain spaces and the timing of it, he was great and got in great positions to score.
“He was unlucky not to score but he was very physical when he needed to be, so I was very pleased with him.”
After missing out on the Premier League title to Pep Guardiola's side in the final weeks of last season, Arsenal will hope the additions of Havertz and fellow summer recruits Jurrien Timber and Declan Rice will give them the needed boost to claim the title next season.