The England striker put the visitors ahead with a tap-in early in the second half before doubling their lead with a header just minutes later.
Despite their dominance, the Blues were frustrated until the interval having wasted several first-half opportunities.
Drew Spence scored a third with a quarter of an hour left to keep Chelsea’s perfect start in Group D.
Palace manager Dean Davenport said: “It was really positive. We defended really well against one of the best teams in Europe.
“We contained them for 45 minutes through our defensive shape. Second half you can see they went up a couple gears to get two early goals.
“From my perspective the goals were mistakes from ourselves to let them back in, but on a positive note we played really well as a team.
“We worked really hard in the week after the Sheffield game because we knew what Chelsea were going to bring.
“Not to concede [in one half] against a team of that quality is a massive boost for us and hopefully that will help us in the games we’ve got coming.”
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PICTURES BY KEITH GILLARD