Wanderers' former record signing took only nine minutes to head in his 13th Premier League goal when despite off side appeals, the former City striker was played on by Andy O'Brien.
And Deco's spectacular second 12 minutes later ensured the Londoners an 11th consecutive league win on their travels.
It might have been different had Kevin Davies not wasted a great headed chance from Gavin McCann's corner before Anelka struck.
And despite plenty of second half pressure, Gary Megson's team couldn't find a way through.
They weren't helped by referee Howard Webb. Three times Bolton had good appeals for penalties turned down including two for handball against John Terry.
But Mr Webb, who sent off Cristiano Ronaldo for the same offence in the derby, chose to ignore the protests.
Talking about the penalty shout after Terry appeared to handle the ball after a Johan Elmander half-volley Bolton boss Megson said: “I’ve said it before, and I’ll reiterate it, but bigger teams get the decisions.
“I didn’t think that that kind of decision would go our way.
“I have to admit I didn’t see it properly. I just saw the shot and our players appeal, but it’s no surprise it wasn’t given.
“It would have been more of a surprise if it had.”
Megson felt the problem, though, was that not enough of his players applied themselves in the first half, and by the time they did, it was too late.
“In the first half there were a few playing at the tempo we wanted and getting after the game in the right manner, but that was not enough,” added Megson.
“The game was a bit tepid from our point of view when it needed to be intense.
“It was better in the second half, but we were 2-0 down, and that was the problem.”
Gary Cahill saw a close range diving header clawed away by Petr Cech-the Czech star's only real save.
However, Deco spurned a one-on-one with Jussi Jaaskelainen as Chelsea eased to a deserved victory.
Bolton ratings:
Jaaskelainen 6, Steinsson 6, A O'Brien 5, Cahill 6, 6 Samuel 6, Muamba 4, Nolan 6, McCann 6, Davies 6, Taylor 7, Elmander 7; subs: Gardner 6 (for Muamba 46), Al Habsi, Shittu, Riga, Smolarek 5 (for Samuel 80), Basham, Obadeyi.
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