Despite the Blues dominating the opening half in west London, a Branislav Ivanovic error allowed in-form striker Michu to fire past Ross Turnbull in the 39th minute.
Chelsea pressed for an equaliser after the break, with David Luiz and substitute Demba Ba coming close.
But Danny Graham capped a memorable night for the Swans when he made the most of a sloppy back-pass from Ivanovic and slotted home.
“We’ve had some historic results already this season but to win here is very special,” Laudrup told Sky Sports. “We had to defend a lot, they had a lot of possession but to be honest they only had three good chances all night.
“They gave us two goals but you have to score them. It was a marvellous fight, we are a team that always try to play but when you play the European champions away you have to change.”
He added: “There is still a mountain to climb, Chelsea have so much quality. We will have to play with the same intensity, they can still win and can score three or four goals against us.”
Swansea captain Ashley Williams was thrilled with his side’s disciplined display but is taking nothing for granted ahead of the return leg at the Liberty Stadium on 23 January.
“We stuck to our game-plan and defended really well,” he said. “We knew it was a massive game for the club but we didn’t get carried away.
“The second goal is a bonus for us and gives us a bit of a cushion. They will come at us though.”
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