The episode saw the Doctor (Ncuti Gatwa) visit a mysterious Barber (Ariyon Bakare), who is using the magic of storytelling in a bid for revenge.
As The Story and the Engine reached its conclusion, it paid homage to the much-loved show's 60+ year history in a sequence of clips that included all of the former Doctors – either via glimpses or audio snippets.
That marks an increase in overnight ratings from last week's episode, Lucky Day, which achieved 1.50 million.
The figure is not consolidated and does not include BBC iPlayer, where it was available at 8am on Saturday, ahead of its BBC One broadcast.
Outside of the news, The Story and the Engine was the BBC's fourth highest rating primetime programme yesterday.
The BBC declined to comment when approached by RadioTimes.com.
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The synopsis for the episode reads: "In Lagos, the mysterious Barber reigns supreme. The Doctor discovers a world where stories have power, but can he stop the Spider and its deadly web of revenge?"
He said: "Storytelling is how the men let each other into their most intimate spaces, but it's also what powers friendships across the world.
"Specifically in barbershops, it is the locomotion that deepens relationships. It is everywhere. It's how we make friends. We begin to tell stories about ourselves to people. But in the barber shop, it is heightened. So storytelling is vitally important."
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