Bellew recovered from a tough start against the Colombian’s mind games and stiff strikes to wear him down from the fifth round onward.
A pair of strong combinations each had Miranda struggling on the ropes in round nine before a belated knockdown was scored with some jarring clean strikes to the body.
Struggling to continue after meeting the count, Miranda was waved off and an emotional Bellew dropped to the canvas in joy.
The win against an experienced former world title contender who came into the bout with a 71% knockout ratio should take the Liverpudlian a long way toward a second world title shot himself.
Bellew, now boasting a record of 18-1, challenged Nathan Cleverly for the WBO light heavyweight strap in 2011 but suffered his first pro defeat in a hard-fought affair.
On the undercard of an action-packed Alexandra Palace bill filled with decisive finishes, Lee Purdy put on a boxing clinic against a game but outclassed Gumersindo Carrasco of Argentina in a fourth-round TKO for the IBF international welterweight title.
Colchester-born Purdy soaked up the energetic Carrasco’s offence into his gloves before picking him apart on the counter, scoring a knockdown at the end of the opening round and two in the fourth before the referee finally called a halt to proceedings.
And Erick Ochieng bounced back after being put under the cosh by Ryan Toms to stop the challenger to his English light-middleweight belt in round five with a series of wicked hooks to the liver in his second successful title defence.
There were also wins for Ryan Taylor, Wadi Camacho, John Ryder, Kal Yafai and Martin Ward, the latter making his professional debut on the card.