The Sherlock Christmas special, The Abominable Bride, has rocketed to fifth place at the US box office despite a limited release, with total international cinema sales exceeding $30m (£21m).

BBC Worldwide said the 90-minute Victorian-themed show, which debuted on the PBS TV network in the US, was screened in 750 cinemas nationwide on 5 and 6 January and grossed $2.7m.

On a per-screen gross ticket sales average, Sherlock topped the US box office over its two-day run, beating hits including Star Wars: The Force Awakens, it added.

“The intention was always to give Sherlock: The Abominable Bride a limited release to amplify the TV moment and create a piece of event cinema for fans to enjoy,” said Sally de St Croix, head of drama brands at BBC Worldwide. “We never expected it to outshine major Hollywood franchises at the box office and couldn’t be more thrilled with the results.”

Sherlock has become a global phenomenon, but nowhere more so than in China where it topped the box office on its first weekend, prompting the BBC to extend its cinema run with sales currently at $20m.

In South Korea, where the film hit the number two spot, The Abominable Bride has so far grossed more than $7m. In Australia it racked up more than Aus$750,000 over its two-day release on the first weekend of the new year. In Europe, the film was aired in Poland and Russia.

In the UK, 18,600 fans watched Sherlock on the big screen despite the episode airing simultaneously on BBC1. The Abominable Bride drew a total consolidated TV audience of 11.6 million, making it by far the most popular show over the festive period.

Doctor Who is made in-house by the BBC and has become one of BBC Worldwide’s bestselling shows. However, the corporation’s commercial arm acts only as an agent for Sherlock’s production company, Hartswood, which is run by Beryl Vertue, mother of Sherlock producer Sue Vertue, who is married to the show’s co-creator Steven Moffat.

“Thank you to all the fans around the world that have enjoyed our special episode,” Sue Vertue said. “I’m pleased to say that preparations for series four are well under way … the game continues.”

Sherlock is licensed to more than 225 territories and The Abominable Bride is set to transmit across many international TV networks. It has so far been screened in cinemas in more than 20 countries.

Filming for the fourth series is scheduled to start this year.