Anelka's excellent opener was his 13th league goal of the campaign so far
Nicolas Anelka returned to haunt his former club with the opener as Chelsea returned to winning ways in impressive fashion at the Reebok Stadium.
The Frenchman put Chelsea ahead when he headed home Jose Bosingwa's cross after nine minutes, and Deco wrapped up the points with a superb scissors-kick.
The Blues had chances for a third, but Bolton responded valiantly late on.
Gary Cahill wasted their best chance, though, as Chelsea set a new record of 11 straight top-flight away victories.
It surpassed the record set by Tottenham in 1960 and Chelsea will be encouraged by the omens as Spurs went on to win the league in the 1960-61 season.
And Luiz Felipe Scolari will know that if Chelsea can replicate their away form at Stamford Bridge they will be in with a shout come next May, for this was a fine win that keeps up the pressure on leaders Liverpool, who also won.
Interview - Bolton boss Gary Megson
The hosts came into the match on the back of four wins in five matches but, with Chelsea unbeaten at Bolton since 1997, the Trotters could have done without Kevin Davies missing a header when unmarked from Gavin McCann's corner.
It was a chance the striker would normally expect to get on target and he was made to pay when, barely a minute later, Chelsea were ahead.
Bosingwa was the creator, the right-back clipping a perfect cross into the area for Anelka to head in off the post to mark his first match against Bolton since his £15m departure with a goal.
Bolton responded but, apart from a Matthew Taylor long-ranger and a series of uncharacteristic flaps at crosses from Petr Cech, rarely threatened.
And on 21 minutes Deco showed the hosts how it is done in emphatic style, the Portuguese playmaker latching on to Michael Ballack's flick with a superb scissors-kick that flew into the corner.
Interview - Chelsea assistant coach Ray Wilkins
Given the Blues' ruthlessness away from home, the second goal was the last thing Bolton needed. Chelsea were able to soak up pressure and hit the hosts on the break, with Deco guilty of a poor miss when he shot wide when through.
However, Bolton refused to give in and, to their credit, caused the odd moment of panic in the Chelsea box.
Twice the visitors had strong appeals for a penalty waved away, first when John Terry appeared to block Johan Elmander's shot with his arm - though it was by his side - and then when the same player handled Davies's header.
Both would have been harsh, though, and it was Cahill that missed the Trotters' best chance, diving on to Davies's flick-on only for Cech to beat his header away from goal.
It proved the Trotters' final chance and their brave second-half display was, ultimately, to no avail, Chelsea seeing out their first win in three matches.
Chelsea assistant first-team coach Ray Wilkins: "It was a great win for us. When we needed to fight, we fought, and when we could we played good football and made some very good chances, so we're delighted.
"We're not too concerned about the record, all we're worried about is silverware so this was all about three points.
"Of course our away form is exceptional but no-one here is worried about our home form. That will come, I'm sure."
Bolton manager Gary Megson: "You can always take positives out of a game once you sit and analyse it but at this moment in time I'm disappointed - not just with the result, but with the way we played in the first half.
"We always try to push on against teams and take the game to them - get in their face, to use a players' expression - but we just weren't intense enough in the opening half.
"Ultimately, it has cost us because you can't expect to give a team like Chelsea a two-goal lead and get away with it. Yes, we did better in the second half, but by then it was too late."
Bolton: Jaaskelainen, Steinsson, Cahill, Andrew O'Brien, Samuel (Smolarek 80), Davies, McCann, Nolan, Muamba (Gardner 46), Taylor, Elmander. Subs Not Used: Al Habsi, Riga, Shittu, Basham, Obadeyi.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.