It was a sixth successive win for the Bulls, who are now just two points off the overall leadership of the competition with a game in hand on leaders the Waikato Chiefs.
But the Bulls, almost assured of a home semi-final later in the competition, escaped with a vital away victory only through the kicking of Springbok flyhalf Steyn, who is soon to depart for France and underlined how much the Bulls will miss his deadly boot.
Steyn kicked six penalties from seven attempts and is now the leading scorer in Super Rugby this season with 181 points.
He showed his usual clam under pressure, no more so than with the decisive kick five minutes from the end, just after the Sharks had gone back into the lead for the first time since the early stages of the match at the Kings Park Rugby Stadium.
The hosts put together a passionate display in the final 10 minutes energised by the only try of a bruising match, a 71st minute effort from scrumhalf Charl McLeod, characterised by ferocious tackling and fierce mauling.
McLeod managed to stretch the ball over the line and apply enough downward pressure to claim the try as he was being virtually swung around in a circle by a desperate Bulls defence.
It was no more than the Sharks deserved for their territorial control and superiority in the scrums, but was not enough to secure them the result.
"But we didn't convert enough of that pressure into points," said captain Keegan Daniel in a post-match television interview.
"We are bitterly disappointed to have lost the game but the boys showed some great fight."
The Sharks stayed 10th on 34 points with only three games left.
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