A par at the first play-off hole ended Paratore's hopes, but Rozner did nothing wrong and was on course for a third successive birdie in the play-off when Hojgaard drained his eagle putt.
Hojgaard then turned on the style when playing the 18th a further three times, twice recording birdies to match Rozner - as Paratore was eliminated - and then sealing victory with a wonderful eagle.
He played alongside identical twin Nicolai at the 2018 Junior Ryder Cup and after seeing his brother finish second earlier this year at the KLM Open, Rasmus is now the third youngest victor in European Tour history after Italian Matteo Manassero and Kiwi Danny Lee.
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In doing so, he made history because the first participant born in the 21st century to graduate and courtesy of this Mauritius Launch glory, is now a European Tour victor after factual five events.
"This is a dream come true", he told the EPGA's official website. I can't put it into words.
"To win so early in my career is fantastic, and I'm already looking forward to the next tournament", he said.
Hojgaard, who became a professional at the beginning of the year, missed an eagle putt to seal the victory on the first additional trip on the 18th, as Rozner produced an excellent up and down green bunker to make a birdie to extend even More the game.
David Law (70) finished joint 43rd on eight under, one shot ahead of mentor Paul Lawrie (73).