Arsenal dominated on a night of woe for former Highbury hero Patrick Vieira, whose second-half booking means he will miss the return leg next week.
The home side had an early scare when Zlatan Ibrahimovic's free-kick was deflected for a corner but Arsenal soon found their feet on a slippery surface and Cesc Fabregas dragged a shot wide.
Thierry Henry whipped a quickly-taken free kick wide and fired another effort just over before the Gunners talisman played a key role in Fabregas' 40th-minute goal, sliding the ball into the area for the young Spaniard to wrong-foot Gianluigi Buffon with a neat finish.
Henry nearly made it two a minute later as the home side began to dominate and Buffon had to be at his best to deny the Frenchman, Fabregas and Alexander Hleb in rapid succession after the break.
But the Juve keeper was left helpless on 69 minutes when Fabregas powered into the area before teeing Henry up for a simple finish.
Jens Lehmann was relieved to see a Mauro Camoranesi chip drift wide - but the winger compounded a dreadful night for the Italians when he was sent off in the 87th minute, with Jonathan Zebina also seeing red moments later.
Juventus will be without their two red-carded players, plus Vieira. It was the complete performance by Arsene Wenger's side and the manager was delighted. "It was everything you want. We had a disciplined performance. We played very well defensively and we played the football we want to play," said Wenger.
"We scored two goals and didn't concede, so that was good. There's still a lot to do, but it was a good start. What is very good to see is this team is enjoying the game. There's a great togetherness in the team."
Wenger felt Vieira had a tough night because of Arsenal's qualities rather than any shortcomings on the Frenchman's behalf. "For me, Patrick Vieira is a great player," said Wenger. "He suffered tonight because we dominated the game. I've no doubt about his qualities."
If there was a tinge of disappointment for Wenger, it was that Arsenal might have won by a wider margin. "I think one more goal was in the game for us and we were not under a lot of threat tonight," he added.
In tonight's other Champions League fixture Benfica held Spanish giants to a scoreless draw at home.