The first half was marred by scrappy play, poor handling and little vision on attack and it ended scoreless.
But the Bulls dominated the first half-hour of the second half, with Steyn, the franchise’s leading points-scorer with 991, kicking penalties in the 43rd, 49th, 53rd, 56th and 58th minutes.
The Bulls physically dominated the breakdown, but their own errors prevented them from gaining much momentum and they showed little ambition on attack, preferring to use up-and-unders by Steyn and the brilliant chasing and aerial skills of wing Bjorn Basson.
Steyn also used the time and space given to him by the strong driving of his forwards to stroke over a 68th-minute drop goal that gave the Bulls a healthy 18-6 lead.
The Sharks managed just two penalties from flyhalf Pat Lambie in the first 70 minutes, but began to keep ball in hand far more effectively during the closing stages as they stretched the Bulls.
The visitors scored the only try of the match as wing Lwazi Mvovo made a strong run down the right, before replacement flank Jacques Botes provided the support to complete the try, which was converted by Lambie.
But the Bulls defence held for the last nine minutes as the 2007, 2009 and 2010 champions made a winning start to the competition.
“It was a combination of eagerness and dew on the ball, but every time we got in their half, we just seemed unable to keep the ball. It was frustrating, but in the second half we picked up our focus and got some points,” Bulls captain Pierre Spies told a news conference after the game.
“There was good defence on both sides and there were no easy yards and no gaps out there. There was a lot of play between the two 10-metre lines and a lot of it was about field position and tactical kicking. The collisions were big, but we controlled the ball well in contact, which was important for us to build pressure,” coach Frans Ludeke said.
Sharks coach John Plumtree conceded that his team did not deserve to win.
“I’m proud of the way we came back at the end, but you can’t win games if you make so many basic errors. Our lineout did not function and we couldn’t dominate the gain-line. They stressed us, their box-kicks were outstanding, and we gave away 14 penalties, so there’s a lot for us to do,” Plumtree said.