Anelka seals top spot for Chelsea
The goal came from a simple move in the 69th minute. With the Porto defenders static, Yuri Zhirkov fed Florent Malouda on the left wing and the Frenchman crossed for his compatriot Anelka to head in unchallenged.
"It's not easy winning at this stadium, but we did it. In the first half we ran some risks and weren't very well, but I think we had a good game, though not fantastic," Chelsea coach Carlo Ancelotti said.
"It was a very important win because it allows us to now concentrate on the Premier League," he added.
Anelka was a threat throughout and created the first chance on 15 minutes with a powerful shot that keeper Beto blocked with some difficulty.
Porto, who like Chelsea had already qualified for the last 16, responded with Argentine midfielder Fernando Belluschi forcing a save from Petr Cech. Striker Radamel Falcao pounced on the rebound but also sent his shot straight at the keeper.
The influential Belluschi had the best chance of a mostly tame first half on 29 minutes, sending a shot crashing against Cech's bar.
The Premier League leaders showed more intent at the start of the second half and playmaker Deco almost netted against his former club on 52 minutes, collecting Rolando's flawed clearance but shooting just wide.
Porto drove forward in search of an equaliser, but substitute forwards Hulk and Ernesto Farias were unable to trouble a composed Chelsea backline.
"No one can forget that we played against a great team, in my opinion the best in English football, with great quality players who always remain serene," Porto coach Jesualdo Ferreira said.
"Porto could have perfectly well drawn this match. Even before Chelsea scored we could have had the first goal, but its the three points that count in the end."
Chelsea have 13 points from five matches with Porto on nine. Atletico Madrid have three and APOEL Nicosia have two.