The actors were both nominated for the accolade after alternating the roles of the monster and Dr. Frankenstein in Boyle's National Theatre production earlier this year (11).
Their joint win marks the first time in the 57-year history of the awards that two actors have triumphed for the same part.
Explaining the decision, the judging panel of critics said it would have been "invidious" not to recognise both Brits.
Sheridan Smith saw off competition from Kristin Scott Thomas to be named Best Actress for her performance in Flare Path at the ceremony, held in London's Savoy hotel.
However, there was consolation for Thomas as British actor Stephen Fry presented her with the Lebedev Special Award for her return to the stage in Betrayal.