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.
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.
"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."
