Phil Bardsley's own goal, a wonderful Jonathan de Guzman strike and Wilfried Bony's penalty - Swansea's first in 56 league games - completely altered the course of the match in just seven minutes.
Chico Flores rubbed further salt in the wound by heading in a De Guzman corner - via unlucky Sunderland striker Steven Fletcher - with 10 minutes to go.
Laudrup said: "In the Premier League it has been a while since we won at home. We have won all three of our home games in the Europa League, but this is our first of the league season.
"We can always talk about who we have played against, and we have played three of the top teams here this season.
"But when people start to talk it is good to turn it down immediately, and the only way to do that is by winning."