Luiz Felipe Scolari's side beat Tottenham's 48-year-old record in the top division and took three more valuable points on the road.
After three games without a win in all competitions, including last weekend's home defeat against Arsenal, the Blues were desperate to return to winning ways.
And that was never in doubt as the visitors struck twice in the opening 21 minutes at the Reebok, despite Wanderers battling efforts after the break.
Bolton old boy Anelka, playing for the first time against his former club since his £15million move in January, handed his new employers the perfect start on nine minutes when the striker met Jose Bosingwa's inviting cross with a diving header for his 15th goal of an increasingly prolific season.
Chelsea all but guaranteed their place in the history books 12 minutes later in the most spectacular of fashions. Salomon Kalou saw his shot well saved by Jussi Jaskelainen but, when Michael Ballack headed the rebound into Portuguese midfielder Deco's direction, he met it with a superb scissor-kick to volley the visitors further in front.
Bolton, the league's form side with four wins out of their last five games, looked anything but against the irrepressible Blues and were fortunate not to find themselves further behind moments later, when Anelka could only find the side-netting after Jaaskelainen's weak punch dropped to the Frenchman six yards out.
Not that Chelsea's dominance would have come as any surprise to Wanderers supporters, who have seen the Londoners win on each of their last five visits to the Reebok Stadium.
It might have all been different had Kevin Davies accepted his early chance but, showing none of Anelka's composure in front of goal, he headed Gavin McCann's seventh-minute corner wastefully over.
Deco and Lampard wasted glorious opportunities to increase Chelsea's lead at the start of the second half.
Deco, in particular, should have wrapped up the points when he was sent clean through by Kalou, but the former Barcelona midfielder fluffed his chance by chipping wide.
Bolton players were screaming for a penalty when John Terry appeared to handle Johan Elmander's volley, but referee Howard Webb waved away the protests on the hour mark.
Gary Megson's side were again appealing for a spot-kick when the Chelsea skipper twice looked like he might have handled it, before Petr Cech made a vital block from Gary Cahill's header as Wanderers tried valiantly, though ultimately in vain, to salvage anything from the contest.