The Pukke used their opportunities and scored one try in the first and two in the second half, but it was a game won by their pack of forwards.
UJ opened the scoring after dominating the opening exchanges when flyhalf Andre Smith kicked a penalty after a illegal tackle. Puk had an opportunity to equalize, but Cecil Dumont's kick from 45 meters out hit the upright.
Smith also missed another opportunity to stretch the lead and last week's hero Trekker van Tonder fumbled the ball after neat interplay between Haas Snyman and Earl Lewis.
A brilliant solo-effort by right winger Andrew van Wyk gave Puk the lead for the first time after left-winger Randall April carried the ball for more than half of the field and Dumont converted from the touchline.
Flanker Jaco Lotter ran the ball back from the kick-off to unleash fullback Willem Barnard and when he was held up Dumont failed with another penalty attempt.
Smith missed another long-range attempt and he had to wait nearly 20minutes to narrow the gap to one point with a similar attempt.
The teams changed side with the Puk holding a narrow 7-6 lead.
After the break Earl Lewis threatened the defence more than once and Dumont missed his third penalty attempt.
There was no love lost among the forwards and they had a full go at each before flanker Jaco Lotter drove over from a lineout five meters out after the UJ was penalized for kicking a player on the ground.
Smith brought the UJ back into range with a left-footed drop-goal.
Wentsley Scott put the matter beyond doubt when he scored in the corner after the UJ tried to play rugby in the own '25 under severe pressure.
Scorers:
Puk: Tries: Andrew van Wyk, Jaco Lotter, Wentsley Scott.
Conversions: Cecil Dumont (2).
UJ:
Penalties: Andre Smith (2).
Drop-goal: Smith.