The Saints extended their unbeaten run of six matches on the road this season as Dusan Tadic's strike from the penalty spot was enough to secure the three points against the Black Cats after Ryan Bertrand was fouled in the area by Yann M'Vila.
Koeman told BBC Sport: "This is a well deserved result. The penalty was well taken and that brings three points, a second clean sheet in a row and we're still unbeaten away from home. I think that's fantastic."
The result leaves Southampton in seventh place in the Premier League.