The Bulls bench at the end pulled them through a hard-fought contest at Loftus on Saturday.
The teams was evenly match and were only able to start pulling away from the Lions when their bench started to come on in the second half.
They added two more tries to eventually beat the Lions 24-9.
The Bulls started the match with a bang and it did not took long for the men in blue to get the scoreboard ticking over.
They broke the Lions defence with Smith getting over for the first try of the match and a 7-0 lead for the Bulls.
The Lions slowly got into the game and two penalties from Fred Zeilinga made it a one point game after 23 minutes. The Lions had a good period after the Bulls dominated the first 10 minutes in the match.
The Bulls had a few opportunities but decided to go for an attacking linnet rather than to go for points. The Lions defence was good enough to keep them out with everything they threw at them.
Swanepoel thought he got over the line for their second try but after a TMO review a knocked on from Papier was spotted which overturned the try.
Both teams had enough opportunities to get some more tries but they were guilty of poor handling and poor decision making on attack.
The teams went into the break with the Bulls leading the Lions 10-6.
The second half both teams found the conditions challenging. The Lions had the early dominance in the second half but the Bulls defence were up to everything the Lions threw at them.
Fred Zeilinga close the gab with a penalty but missed two in a period that they were keeping the Bulls in their own half.
Poor discipline from the Lions started cost them. With a deliberate knock down by EW Viljoen the referee had no choice to send him to the bin.
The Bulls got Stravino Jacobs over in the corner but the try was again overturned by the TMO for obstruction at the Bulls maul.
The Bulls finally got the try when Burger found space through the Lions defence which Steyn converted to give the home side a 17-9 lead.
The Bulls stayed in the Lions half of the field and a death touch from Morne Steyn kicking for the Madosh Tambwe in the corner saw the winger go over but it was yet again overturned by the TMO.
The Bulls really stepped up with their bench in the final quarter of the match dominating play on attack and keeping the Lions pinned in their own half. The only aspect where the Lions dominated was in the scrums.
With Morne Steyn keeping the Lions in their own twenty two with his kicking game it was just a matter of time before they got over the whitewash.
Elrigh Louw scored the last try of the match just before the hooter. Steyn converted the try to give the Bulls a 24-9 win in the first round of the Guinness PRO14 Rainbow Cup SA
Bulls: Tries – Chris Smith, Zak Burger, Elrigh Louw Conversions – Chris Smith, Morne Steyn(2) Penalties – Chris Smith
Lions: Penalties – Fred Zeilinga(3)