Bordeaux were tame opposition, with Chelsea keeper Petr Cech not forced into serious action at any point, but it was still an impressive show as the Premier League leaders continued the form that has taken them to the summit.
Chelsea boss Luiz Felipe Scolari, predictably, named the same team that outclassed Manchester City on Saturday - and they continued in imperious form.
It took last season's runners-up only 14 minutes to take the lead, Lampard arriving in a central position only six yards out to head Bosingwa's superb cross beyond Ulrich Rame.
Scolari demands improvements
Rame then saved well from Anelka and John Terry headed Lampard's free-kick just wide before Joe Cole deservedly doubled Chelsea's advantage on the half-hour.
Lampard swung a corner into the near post and the England midfield man rose above the Bordeaux defence to glance home a neat header.
Lampard should have piled on the misery for Bordeaux three minutes later, but he uncharacteristically dragged a simple finish wide from close range.
Bordeaux, as they had to, showed greater ambition after the break and Fernando gave Chelsea a moment of anxiety after 50 minutes when he shot just wide.
Scolari, with the game seemingly under control, decided to make a change on the hour when he sent on fit-again Michael Ballack for Deco.
And Anelka should have wrapped things up almost immediately, but he shot into the side-netting from an angle.
Chelsea had taken their foot off the gas after the break and Scolari went through his full range of arm-waving as he became increasingly agitated with his side.
And his theatrics had the desired effect as they scored a beautifully fashioned third with eight minutes left.
Always room for improvement - Ballack
Jon Mikel Obi opened up the Bordeaux defence with a powerful surge, and when Lampard released Malouda with a clever flick, the Frenchman fired an emphatic left-foot finish across Rame.
Ricardo Carvalho then headed against the bar and Anelka drove inches wide as Chelsea ended the game as they begun it, in complete control.
And they rounded off the night in style when Anelka slotted in a simple fourth after substitute Juliano Belletti's long-range shot rebounded into his path off the bar.
Chelsea manager Luiz Felipe Scolari
"We started very well, we got three points but we made too many mistakes.
"We did not control the game enough, we let them have too much of the ball, especially in the second half, but we did get two late goals. However, the most important thing was the result.
"Frank Lampard loves football, he trains hard every day and when you do this God helps you.
"If you didn't do this in training you would not do well in the match.
"OK, the result was good and it is important to win but we made too many mistakes."
Bordeaux coach Laurent Blanc
"We always knew it was going to be tough if Chelsea opened the scoring but it was frustrating they took the lead from a situation - with Frank Lampard getting on the end of a cross - that we knew all about.
"It was also frustrating that a little guy like Joe Cole can get in front of two or three big blokes in defence and head it in.
"We knew we were playing a top side but we should have shown a bit more physical effort and commitment. It's disappointing. We battled so hard to get into this competition and we didn't seem to be aggressive enough or up for it tonight."
Chelsea: Cech, Bosingwa, Carvalho, Terry, Ashley Cole, Obi, Joe Cole (Belletti 74), Deco (Ballack 61), Lampard, Malouda (Kalou 84), Anelka.
Subs Not Used: Hilario, Di Santo, Ferreira, Alex.
Goals: Lampard 14, Joe Cole 30, Malouda 82, Anelka 90.
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