"In the second half we bossed them - it's how we should have been. We asked more difficult questions.
"You need to show every week that you ready to fight for the result. We did it in this game."
The defeat will keep pressure on Swans manager Francesco Guidolin, whose side have lost five of their last six in the league and sit just above the relegation zone.
"My team played a very good game, Liverpool is a very strong team," he said. "The draw would have been the right result."
Chelsea steadied their ship after two straight losses.
Willian put the Blues in front in the second half and Diego Costa clinched the three points with his league-best sixth goal.
West Ham avoided a fifth straight loss with a 1-1 home draw against Middlesbrough. Dimitri Payet cancelled out an opener from Boro's Cristhian Stuani at the London Stadium.
West Ham remain winless in five and in the bottom three on goal difference behind Swansea.
Winless Sunderland moved off the bottom of the table with a 1-1 home draw against West Brom.
Substitute Patrick van Aanholt's goal seven minutes from time lifted the Black Cats above Stoke on goal difference.
Watford twice came from behind to draw 2-2 with Bournemouth with Isaac Success netting the second equaliser.
Manchester City look to make it seven wins from seven when they visit Tottenham, Manchester United host Stoke, champions Leicester take on Southampton and Burnley welcome Arsenal in Sunday's games.