"Take nothing away from Subriel - he's a great champion.
"I didn't really stick to the tactics tonight. I played him at his own game. You can't hurt me and I knew I'd get to him."
Smith joined heavyweight Fabio Wardley, welterweight Lewis Crocker, super-featherweight Jazza Dickens and featherweight Nick Ball as the UK's fifth current male world champion.
Ticket sales were reportedly modest, but there was no shortage of noise from travelling supporters as Smith walked to the ring to 'When the sun goes down' by Arctic Monkeys, who are from his home town of Sheffield.
Yet it felt like a home fight for Matias, with New York's strong Puerto Rican population firmly behind the 33-year-old.
He appeared so relaxed that he stopped for selfies with family members during his ring walk.
Making the first defence of the title he won against Alberto Puello in July, Matias has at times been a slow starter and Smith exploited that by banking the opening round with sharp, crisp punches to head and body.
Matias edged the second, forcing Smith on to the back foot as blood trickled from the Briton's nose.
After a scrappy third, Smith, remarkably and unexpectedly, chose to trade with the champion.
With 22 knockouts in his 23 wins, Matias entered with a reputation for relentless pressure and heavy hands. Smith, however, also carried stoppage power, having recorded 13 knockouts of his own.
He landed several heavy left hooks to close the fourth round. Then came the career-defining moment that truly announced Smith on the world stage.
After briefly stumbling from a Matias combination, an unfazed Smith came roaring back in a fifth-round firefight.
He landed two straight left-right combinations that snapped Matias' head back, before the decisive overhand right.
There was a brief protest from Matias at the referee's decision, while Smith's trainer and father, Grant Smith, rushed into the ring in celebration.