The BBC said the feature-length opening attracted a third of all viewers who were watching TV during that time slot, an average of 6.8 million.
However, the new Time Lord's introduction to audiences attracted mixed reviews from critics.
Some praised him for being "brash, furious and very, very Scottish" and "suitably darker and more mature", while others said he had failed to "stamp his personality on things" and described the show as a "lacklustre affair".
Glasgow-born Capaldi is the 12th actor to play the Doctor in six decades of the Doctor Who series. At 56, he is also the oldest since the first, William Hartnell.
Perhaps best known for his role as a foul-mouthed spin doctor in The Thick Of It, he has taken over from 31-year-old predecessor Matt Smith.
Doctor Who fans saw a new complex Doctor and there were differing reactions on Twitter to the first dose of this darker, more prickly Time Lord.
One viewer, Alex Hunt, said: "Bit disappointing when your favourite part of a new episode with a new Doctor is when the old one calls in for a cameo."
Paul Ilett described it as a "Great opener for Peter Capaldi in #doctorwho - more character, more emotional depth. Feels like the show's back on track."
And Samantha Jayne tweeted: "So impressed with that episode. Didn't feel like a kids show for once, it felt like a drama. Complex characters, awesome script."