The series has been warmly reviewed, with past Doctor Who Sylvester McCoy telling the BBC News website he was "captivated" by the partnership between Eccleston and Piper.
Doctor Who's comeback helped ramp up the usual Saturday ratings battle between BBC One and ITV1.
The Time Lord's comeback was pitted against Ant And Dec's Saturday Night Takeaway on ITV1, featuring England captain David Beckham as a special guest. It attracted 7.2m viewers, peaking at 8.5m.
An ITV spokesman said: "The audience for Ant and Dec was up on the show last Easter Saturday, which got 7.1 million viewers, so we have no complaints."
Graham Norton's new ballroom dancing show, Strictly Dance Fever, went toe-to-toe with ITV1's Stars In Their Eyes Live Final - both shows appearing twice in the evening.
The early edition of Strictly Dance Fever attracted an average of 4.9 million people, peaking at 6.3 million, while Stars In Their Eyes, hosted by Cat Deeley, pulled in 5 million people, peaking at 5.6 million.
Later in the evening, Strictly Dance Fever's results show had an average of 4.7 million viewers, peaking at 7.2 million. On ITV1, Stars In Their Eyes had an average of 5.5 million viewers, but peaked at 6.3 million.
However, the Time Lord had Graham Norton breathing down his neck too, as a technical problem meant the sound from Strictly Dance Fever was briefly played over the opening scenes of Doctor Who.
"There was a technical problem which was resolved as quickly as possible," a BBC spokesperson said.
"We apologise if it affected viewers' enjoyment of Doctor Who."