Kai Havertz opened the scoring before Bukayo Saka doubled the advantage, while Martin Odegaard added a third after half-time as the champions quickly showed why they are among the favourites to retain their crown.
New signing Christos Tzolis also made an encouraging league debut, causing Coventry problems down the left and playing a key role in Arsenal's second goal.
Havertz put Arsenal ahead when Riccardo Calafiori delivered a low cross into the penalty area following good work from Tzolis. The Germany international calmly finished to give the hosts control.
Arsenal continued to dominate and doubled their lead before half-time. Declan Rice found Tzolis, whose low cross proved too difficult for Carl Rushworth to hold. Saka reacted quickest to the loose ball and tapped into an empty net.
Coventry briefly threatened when Loum Tchaouna produced an overhead kick that landed on top of David Raya's net, but Arsenal remained firmly in control.
Odegaard then made it 3-0 after the restart. Ben White's pull-back was scuffed towards goal and Rushworth lost his footing as the ball crossed the line.
Arsenal were able to manage the rest of the match comfortably, with Mikel Arteta taking the opportunity to substitute several key players to standing ovations.
Arteta was particularly pleased with the hunger his players showed at the start of their title defence.
"They look exactly the same as last season to me," Arteta said. "What I did transmit to them was to show more desire and earn the right to be better than everyone else."
The Arsenal manager added: "There was a lot to like from the performance. It was a great result but also the manner we started the game.
"It was domination, clarity and understanding. It was really impressive."
Arteta also praised the way his players combined in attack.
"We were so dominant, we had incredible connections, we were really accurate with the ball," he said. "The players have to be decisive, and they were today. They looked really connected and played with a lot of purpose."
Odegaard was delighted with Arsenal's start and believes the squad has the quality to challenge for another title.
"The perfect start. Three goals and a clean sheet. It was really solid," he said.
"The team's quality is unbelievable; we see that every day in training. The level we compete at is unbelievable, and we all push each other."
The Norway international insisted Arsenal are not simply trying to protect last season's achievement.
"We don't feel we have to defend anything. We want to do it again, and that's the mindset," Odegaard said.
"Last year is finished now, we want to do it again, and we want to attack it and fight for it again."
Arsenal also confirmed the signing of Aston Villa defender Ezri Konsa, while Arteta revealed that Bruno Guimaraes' injury is not expected to keep him out for weeks.
For Coventry, the night provided a difficult introduction to life back in the top flight after 25 years away.
Lampard accepted that his side had been given a clear indication of the level required to compete with the champions.
"Fantastic team, a good lesson for our boys to see the levels. They played like champions," Lampard said.
"It was a difficult game for us. The experience of it is probably good for us in terms of the stadium, the atmosphere at the start of the game, the quality that they have.
"When you concede goals, not great from us, and that's the reality."
Coventry struggled to create any sustained threat, taking until the 60th minute to record their first touch inside the Arsenal penalty area.
For Arsenal, however, the opening night could hardly have gone better.
