It remains to be seen whether the cut will affect Parker in the future. He is only 21 and young skin heals better than battered tissue on older fighters. But eyebrow cuts are tricky and sometimes require complicated plastic surgery - which he will now have in the US - to stop splitting when the area is hit again. A canny, fast-hands fighter will pepper a cut area to get the blood flowing and get the fight called off.
Parker has some rarely-seen attributes for a heavyweight - fast hands, good movement, a sapping jab and some sizzling combinations; the work he is doing with Las Vegas-based trainer Kevin Barry is centering on controlling the distance between him and his opponent - something not easily achieved in a toe-to-toe slugging match.
He is also increasingly showing the killer instinct inside the ring and is an intelligent and amiable young man keen to learn and succeed. He also showed a new weapon against Tatupu - a much improved left hook, although it was the right hand that finally caught the game Samoan.
Twice now Parker has stepped up his momentum and punching power at the business end of a fight - once to put the bout against Brice Ritani-Coe in Los Angeles past any doubt and on Thursday against Tatupu. Warned that the fight could be called off because of his blood flow, Parker knew he had to floor Tatupu in the second round and did so with a flourish of big, fast punches.
He will likely not get the same latitude from his next opponent, Arias. Also a shorter heavyweight, 39-year-old Arias has a reputation as a durable and dangerous opponent.
Boxing analysts rate him as a tough opponent who will not be easily floored or dissuaded from his stalking style where he relentlessly moves forward, putting his opponent off his rhythm and sapping confidence with his assault. Parker has not fought anyone like this before; it will be a test.
Think the Argentinian heavyweight from the Muhammad Ali era, Oscar Bonavena. Like Arias, only about 1.81cm tall, Bonavena could take a punch and wore his opponents down with his stubbornly aggressive style. In their first fight, Bonavena had a young Joe Frazier down twice (though Frazier rallied to win) and only Ali ever knocked Bonavena out in his 68-fight, nine-loss career.
Arias has fought 64 times in a 17-year career, with most of his wins over South American opponents little recognised in this part of the world. He has lost 11 times.
He has also met a couple of bigger names - losing to former British heavyweight hope Audley Harrison after taking the fight with four days' notice. Arias has also only been knocked out twice - by big Cuban Juan Carlos Gomez (who went on to fight Vitali Klitschko, losing the fight for the WBC world title in 2009 by a TKO in the ninth) and by the "fast hands" Fres Oquendo, one of David Tua's victims in 2002.
But Arias has now won his last 12 fights, many against young, inexperienced contenders and all defending his Brazilian and South American titles. Even though he is not a big name, Arias will be a step up for Parker.
