The Bulls showed dominance up front with their forwards, but could not convert that into a larger margin on the scoreboard as they allowed the Australian side to creep back into the contest.
Fullback Warrick Gelant and number eight Duane Vermeulen scored the Bulls' other tries, both inside the opening quarter, before Matanzima popped up with what proved the winning score 10 minutes from time.
Scrumhalf Nick Phipps, fullback Kurtley Beale and wing Curtis Rona all crossed for the Waratahs, who capitalised on errors from the home side to stay alive, but could not pull off what would have been a morale-boosting victory.
The Bulls' cause was not helped by handling errors and an inability of the backs to take advantage of the excellent platform that had been laid by their tight-five.
They move to the top of the South African Conference with 28 points, while the Waratahs stay in fourth in a tightly-contested Australian pool.
Gelant crossed for the first try on 11 minutes when he spotted a huge gap in the Waratahs defence and coasted in to score.
But that advantage would last only a few minutes before excellent breakdown work from Karmichael Hunt allowed Phipps to score.
Vermeulen was all poise, pace and power as he claimed an intercept 55 metres from the Waratahs tryline and sped away to dot down, holding off tackles from the retreating visiting defence as he did so.
The Bulls led 18-7 at halftime, and advantage that was extended by three points as flyhalf Handre Pollard landed a penalty.
But then began the fight back from the visitors, as first Beale crossed and then Rona was afforded acres of space to bring the scores level at 21-21 with 12 minutes to play.
But the decisive moment in the game came shortly afterwards as Matanzima scored a first Super Rugby try when he ran a good line and barged over from close-range.
(Reporting By Nick Said; Editing by Christian Radnedge)
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