The 2-1 win reduced the gap to the top four for last season's champions to two points, but Tottenham can extend it if they win at Bournemouth on Sunday.
It was Martin Kelly who found his own net to double our lead soon after Willian's opener, and the fact we didn't score again was a surprise considering the volume of efforts throughout the evening.
A week after their limp surrender at the Etihad, Chelsea reminded Conte how convincing they can be when they play with objective on the front foot, even if Barcelona are more than capable of making them pay for the level of ambition they showed against Palace. They dominated the ball and had seven attempts at Wayne Hennessey's goal in the opening 20 minutes, albeit without truly testing the Palace goalkeeper.
FW Olivier Giroud, 7 - Denied a goal when James Tomkins cleared off the line, Giroud might also have scored on several more occasions if it wasn't for some poor luck. The move deserved a more elegant finish as the ball sped from Cesc Fabregas out to Marcos Alonso on the left, and then infield towards Willian. They have now lost all of their last three games and they have a tough task this weekend when they travel to Stamford Bridge for a mini-derby in London. Conte's team was giving the home fans something to sing about.
Palace did pull a goal back through Patrick Van Aanholt in second-half stoppage time, but the Blues managed to hold on for the win.
Chelsea almost took advantage of that let-off, but Tomkins threw himself in the way of yet another goal-bound shot, this time from Willian, and Hennessey saved from Hazard.
Willian's goalscoring form continued in Chelsea's next match at Manchester United and the Brazilian made it 13 for the season in all competitions - a career-best - in Chelsea's 2-1 victory over Crystal Palace on Saturday.
Zaha caught Andreas Christensen dallying in his own half and played in Alexander Sørloth, one on one with Courtois.
The Norwegian must have thought his first goal in English football was a formality, but he hit his shot against the post.
Merson added: "But I think without Wilfried Zaha they really struggle, so I can't look beyond Chelsea".
Antonio Conte's side is locked with Barcelona at 1-1 heading into the second leg on Wednesday. The French striker was replaced by Alvaro Morata in the 72nd minute but may have pushed himself into contention for a start at the Camp Nou. They are a good team fighting a lot to avoid relegation.