Two late Michu goals were enough to see off an Arsenal side who are struggling badly of late, but that doesn't take anything away from the Welsh team - who Gunners' boss Arsene Wenger admitted were the deserved winners.
A delighted Laudrup praised his side's recent displays, telling reporters: "Three great performances, each one better than the other one.
"We knew after the two last results that we could play without pressure and that there was some pressure on Arsenal. The team is playing with a lot of confidence."
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Laudrup was particularly pleased with the manner in which his side saw off Arsenal away from home.
"Arsenal put us under pressure for 20 minutes in the second half and you know their players can make the difference at any moment, so you can never sit easy," said the Dane.
"We looked in quite good shape and were only defending deep a few times."
The Swans face a tough run of fixtures in December, with in-form Norwich their next opponents, before they take on Tottenham and league leaders Manchester United before Christmas.