Frank Lampard and Joe Cole scored in the first half to set up Chelsea for a relatively easy win in the Champions League group A.
Goals for Malouda and Anelka late in the match made the scoreline a flattering 4-0.
Chelsea boss Phil Scolari wasn't happy with his team's performance.
He said: "We made many mistakes in the second half. We did not control the game enough, we let them have too much of the ball. We did not play very well."
"We could be punished by other teams who get in front of goal faster and with quality. That is dangerous for us."
"When you are winning 2-0 at half-time you need to work the ball and control the game. You don't need to win 5-0."
"We tried to attack without the ball and with no good connections," he said.
"But most important for us is the result."
"It is important to start with a win because in this competition you never know what will happen."
"You see that Cluj beat Roma. That is a warning for us for the next game."
Bordeaux coach Laurent Blanc said: "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.
Booked: Deco.
Goals: Lampard 14, Joe Cole 30, Malouda 82, Anelka 90.
Bordeaux: Rame, Jurietti, Diawara, Planus, Placente, Diarra, Menegazzo (Ducasse 74), Gouffran (Obertan 65), Gourcuff, Wendell, Chamakh (Cavenaghi 65).
Subs Not Used: Valverde, Henrique, Bellion, Traore.
Att: 39,635
Ref: Pieter Vink (Holland).
UEFA Champions League : Group A Table
| 1 | Chelsea | 1 | 1 | 0 | 0 | 4 | 0 | 4 | 3 |
| 2 | CFR Cluj-Napoca | 1 | 1 | 0 | 0 | 2 | 1 | 1 | 3 |
| 3 | Roma | 1 | 0 | 0 | 1 | 1 | 2 | -1 | 0 |
| 4 | Bordeaux | 1 | 0 | 0 | 1 | 0 | 4 | -4 | 0 |
