With his father looking on from ringside, the 23-year-old was far from faultless but was awarded the referee's decision 80-73 - a margin that was harsh on 31-year-old Pryce.
Eubank Jr began with some neat and tight work in the first round - moving cautiously and jabbing sharply with Pryce struggling to adjust to the speed of his man.
A pair of rocking Eubank Jr right hooks were the highlights of the second as he began to throw one-two combinations, although Pryce asserted himself to a degree before the bell.
Eubank Jr's speed was there for all to see early in the third as he put together some flashy combinations that brought cheers from his supporters, but his naivety was equally evident as he let Pryce stun him slightly with a solid shot in the final minute.
The fourth saw a return to more sensible tactics as Pryce was forced to suck up some meaty bodyshots from his opponent, and the veteran's nose was soon bloodied as Eubank Jr warmed to the task.
There was some slightly premature showboating from the youngster after Pryce had arguably edged a close fifth session, although a jolting Eubank Jr uppercut was the most eye-catching punch of the round.
Eubank Jr continued the needless showboating and gesticulations in the sixth - seemingly content to put rounds in the bank and suck up apparently harmless shots coming from Pryce.
There was no doubting the snappiness of Eubank Jr's jab in the penultimate round but it was not until the final minute that he strung together a combination of punches with Pryce clearly working the harder.
Both fighters ran risks in the last with the fight seemingly still on the line, but neither could produce a killer blow as the youngster added an eye-catching name to his record.
Eubank Jr said afterwards: "Every time I come out here, I want to prove to the fans and make a statement that I'm the real deal. This isn't a joke. It isn't a gimmick.
"Sure I could go out there looking for the knockout and throw haymakers in the first and second rounds, but I don't want to do that - I want to learn and get the rounds under my belt."
Eubank Senior added: "The fellow (Pryce) had 33 wins and from Christopher's viewpoint, in another five fights he's going to be speaking only about James DeGale."