The Swans claimed all three points at Liberty Stadium to climb out of the relegation zone, thanks to a first-half header from skipper Ashley Williams, prompting a jubilant reaction from Curtis, who will know work alongside new head coach Francesco Guidolin.
"In the first half especially we controlled the game and it was one of our better performances of the season," said Curtis on Sky Sports.
"It was a little bit tense in the second half, we could have done with a second goal and maybe then we could have established a bit of supremacy, but it was a huge three points and credit to the players.
"The crowd played a huge part too. They defended every ball into the box as well.
"Everybody is delighted; it's the start of a long road until the end of the season."