In the process, he became the fourth player in Super Rugby history to score 1000 points, after Dan Carter, Morne Steyn and Stirling Mortlock.
But Bulls first five-eighth Handre Pollard charged down a chip from opposite Ihaia West to spark a sweeping move which resulted in the decisive try for Schoeman.
Pollard's two penalties were important in putting his team in front in the first spell. They scored early through winger Johnny Kotze but the Hurricanes replied through hooker Ricky Riccitelli from a lineout drive and winger Wes Goosen from a chip and chase.
The Bulls scored the try of the game from inside their own half just before the break, when Springboks forward Lood de Jager galloped over after a bust and loping run from fellow lock RG Snyman.
That try came when the hosts were reduced to 14 men, with Schoeman shown a yellow card for a high shot.
The Hurricanes' fitness levels appeared to lag in the thin air, with their error count and concession of penalties problematic in the second spell.
They were out-pointed in areas they would normally expect to shade the youthful Bulls side, such as running metres and offloads, leaving room for improvement ahead of next week's clash with the Jaguares in Buenos Aires.
- AAP
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