The Brazil international opened the scoring in the 25th minute, darting in off the left flank and finding the bottom-left corner via a deflection, with a Martin Kelly own-goal coming soon after.
Although Willian did not manage to add to that, his opener was his fifth in his last five games across all competitions, while he generally caught the eye throughout.
One particularly impressive moment in the second half saw him enjoy a sensational solo run through Palace's midfield, before eventually seeing a seemingly goal-bound effort blocked in front of the target.
And Conte commended him for his display, both on and off the ball.
"You can see that if a player stays in great form I'm the first to pick him in the starting XI," Conte told reporters in his news conference.
"Willian is playing in a fantastic way, but I want to underline, not only with the ball, also without the ball.
"He's working very hard and he's helping the team without the ball. He's showing great maturity at this point of his career.
"In my heart I hope to see him at this level, to continue this performance. He's playing very well with the ball, without the ball.
"It's important to have balance within the game, because when we lose our balance it's very difficult."
Chelsea travel to Camp Nou having rescued a 1-1 draw at Stamford Bridge last time out and Conte acknowledges his team will be facing one of the world's best sides.
"We have to show great resilience," Conte added. "The game will be totally different.
"We are playing against one of the best teams in the world. We have to try to have the same focus, the same attention as the first leg against Barcelona.
"We played a really great game. It was almost the perfect game. It won't be easy. At the same time we have to try the right solution to play this game.
"The best way sometimes is to speak with the players and to try to find together the right plan to face this game."