The unbeaten Manchester-based fighter hurt Rogan badly with a series of body shots at the close of the round. Rogan just beat the count but his corner decided to stop the fight against Rogan's will.
It was an impressive finish from Fury after a disappointing opening couple of rounds when he surprised everybody by coming out in a Southpaw stance.
Rogan seemed a lot less bothered by the tactic than Fury and the 40-year-old Commonwealth champion clearly won the first two rounds to the delight of his hometown crowd.
Fury though started to find some joy in the third and put Rogan down by following a couple of right jabs with a power left.
He then ended the fight with another powerful left – this time to the body to move his record to 18-0 (13KOs).
"Just practicing a few things in there, I'm a world class heavyweight and I'm trying new things," said 23-year-old Fury of his change of style in the fight when asked by Channel 5.
"It felt like home here….and I hope to bring big title fights to Ireland," said Fury who was eligible to fight for the Irish title as both his parents are from the country.
The bout was supposed to be for the WBA lightweight title but Rios failed to make the 135lb weight for the second fight in a row.
And, despite being sluggish and scrappy throughout, Rios was judged to have won with scores of 116-112 and 115-113 in his favour; a decision that angered many fans at the Mandalay Bay Resort and Casino.
The third judge called the fight 117-111 in favour of Abril, who dominated several rounds with superior aggression and cleaner shots.
Rios’s next fight is likely to be against
Marquez, who also holds titles in featherweight, junior lightweight and lightweight divisions, won the bout with scores of 119-109, 118-110 and 118-110 to make amends for his narrow loss to Manny Pacquiao last November.