The chiefs of the corporation feared whether the new series with a new lead writer and an all-new cast would continue to attract a large audience.
The new programme however drew eight million audiences, a figure matching the first episode of David Tennant, Matt's predecessor.
Matt Smith, 27, who played the Time Lord, is the 11th actor to take the role of a travelling doctor. The Doctor's sidekick Amy Pond, played by Karen Gillan, was also hailed by many.
Audience figures for the show peaked at 8.4 million and averaged 8 million, the BBC said.
A poll on the Digital Spy website showed that 67 per cent viewers rated the show as "very good".