Alex Oxlade-Chamberlain scored the winner with a powerful drive into the top corner with his weaker left foot.
Ramires headed wide unmarked from Loic Remy's cross as Chelsea failed to hit the target before the break.
Eden Hazard skied a chance over the bar before Oscar's free-kick was parried wide by Arsenal debutant Petr Cech.
It was the first time the former Chelsea goalkeeper had been called into action - after 68 minutes of play - and soon after he comfortably held on to Kurt Zouma's header.
Arsenal went close late on through Santi Cazorla and Kieran Gibbs in a match where both sides looked rusty a week before their Premier League opener.
Oxlade-Chamberlain's stunning strike was Arsenal's first goal against Chelsea for 506 minutes, a run that stretched back to 2007, as the Gunners ended the Blues' eight-match unbeaten run against them.
Post-match reaction
Arsenal boss Arsene Wenger, speaking to BT Sport: "We have suffered physically today and the pitch was not great.
"But overall it's good because in pre-season we have been solid defensively. Pre-season has gone quite well.
"We have no big injuries at the moment apart from Jack Wilshere who we lost yesterday."
Gunners midfielder Alex Oxlade-Chamberlain, on BBC Radio 5 live: "It's really nice to come to Wembley and win. We wanted to keep our good streak here going. We are delighted to win another trophy and for me personally, I'm happy I got the winner.
"I don't actually think I've lost at Wembley. Long may it continue. Today was a big game for us and we wanted to lay down a marker for our manager and our fans. I want to contribute more goals this season, it's a target I've set for myself, and of course I'm happy to have got the goal today."
Chelsea manager Jose Mourinho on BT Sport: "We were the best team. We had more initiative, we controlled the game by having ball possession. Arsenal defended with 10 players, they put everybody in front of their own line and they had good organisation, congratulations to them.
"They had a couple of chances in counter attacks but we had ours in organised football. They played their game tactically and found themselves one goal in front without any reason.
"This season the Premier League title is very difficult but it is very difficult for everyone. The way other teams are spending they have big power in the hands while we are the same as last season. And with that we are going to try."