Willian shone as the Blues closed the gap on the top four but Patrick Van Aanholt provided a late scare by netting with only a few minutes remaining.
Antonio Conte’s men still sit two points outside the Champions League places, with Tottenham yet to play this weekend.
But the Blues boss admitted he was pleased with the performance of his side.
“I think that we created a lot of chances to score a lot of goals today,” Conte told BT Sport.
“We conceded 2-1 at the end and there’s a bit of pressure but did well to keep the ball high up the pitch way from our box.
“I think we deserved to win, we played a good game, especially in the first half against a good Crystal Palace.
“They are a good team fighting a lot to avoid relegation.”
Chelsea now have a huge task ahead of them when they take on Barcelona on Wednesday evening.
The Blues held the Catalan outfit to a 1-1 draw in the first leg.
“We have to prepare for that game in the right ways, they are a strong team, the game will be totally different compared to today but we have three days to decide with the players the right plan,” said Conte.