Playing away from home, the Madibaz went down 19-12 in a hard-fought match that remained in the balance until deep into the second half.
After the match had been suspended early in the first half due to heavy rain and lightning, the visitors came out in full attack mode but were unable to break through UJ's defences.
The home side led 6-3 going into the break with just one penalty separating the teams.
"The boys had certainly put their bodies on the line, but we are hurting," said Madibaz head coach David Maidza.
"It is a bit unfortunate not to have come away with more than just one point. It was a match for the taking."
Maidza said the team defended valiantly, but were not clinical enough when they had the ball in hand.
"I felt it was a true team effort with everyone putting their hand up, but we could have done better with the possession we had."
He said the players could have asked their opposition more questions, but pointed out that it was a "learning curve" for the relatively inexperienced outfit.
Having lost 42-13 in the corresponding fixture last season, Maidza will be upbeat after a much-improved performance against the Highveld side.
Following the match, he said that he had identified "a couple of issues" on attack and will focus on these with his players during the video analysis sessions this week.
"It is early in the season and there is still time to improve. We've got to fight for it."
The Madibaz will kick off their home campaign against Maties in a televised match in PE on Monday evening.
Go to Facebook and Twitter for more Madibaz news.