The Scot, who plays the 12th incarnation of the Time Lord, won 7.3 million viewers for his debut story on August 23.
However, the show garnered about half the audience of the X Factor on Saturday night, with only 5.3 million viewers tuning in compared to 10.6m for the ITV show, which overlapped it.
In his second episode, Capaldi faced off the menace of a Dalek fleet of space ships in his first meeting with the aliens from Skaro.
The viewing figures compare with around 6.4 million who watched the first episodes of predecessor Matt Smith's final series last year. However, Capaldi's debut was the best-watched season-opener in four years.
Predecessor Sylvester McCoy last week backed him, adding: "You can tell he's an accomplished actor."