Niggling injury problems ahead of the match threatened to derail Dortmund's bid to overcome an Arsenal side that it failed to beat on home turf twice in the previous three seasons.
But Italy striker Ciro Immobile made the most of his recall to the starting line-up with a first goal since his close-season move from Torino.
Pierre-Emerick Aubameyang's pace and directness typified Dortmund's thrilling approach and the in-form forward gave the Group D pacesetters breathing space in the 48th minute.
"I'm very pleased," Klopp told Sky Sports. "Three players went out of the team because of little muscle problems but in the morning we made some decisions and brought the other players in.
"I have to say it was a really great performance from my team. It was pressing and counter-pressing - perfection; it was really strong."
Explaining his high praise, Klopp said: "We were brave, we were fast - everything we need for this game.
"If you give them one metre of space they are so strong. I saw some counter-pressing situations in the centre of midfield that were perfect.
"For this game you need to be brave. Against these strong players we had to look for one-to-one situations.
"I enjoyed this game from the first second until the last."
Dortmund threatened to run riot following Aubameyang's strike, while Armenian attacking midfielder Henrikh Mkhitaryan was wasteful to the extent that he spoke to his boss afterwards.
"He spoke to me after the game," Klopp explained with a smile. "I said today we didn't need his goals. There will be a time when we need his goals and he will do it."
Dortmund laid down a definitive marker for this season's Champions League, a particularly impressive feat for a club that has lost key players such as Mario Gotze and Robert Lewandowski over recent seasons.
But Klopp dismissed the idea of this representing a new era for his club, laughing heartily before adding: "No, I don't think about this. We did what we had to do to win this game.
"The important thing for me is that it is three days and then we have to play against my former club [Mainz].
"It's hard work all the time but when you see games like this, it's the best job in the world."
