The Pretoria-based Bulls leveled the match with one minute remaining when Johannes Engelbrecht scored a try in the corner from a turnover and Morne Steyn converted.
The South Africans pushed for the win on the ensuing kickoff but were penalised directly in front of their own posts.
Lealiifano, who had only missed one shot at goal in six attempts Saturday, struck the winning kick just inside the left post.
The ACT scrum dominated the Bulls throughout the match, culminating in a yellow card to loosehead prop Morne Mellet in the 65th-minute for repeated scrum infringements.
With the Bulls scrum one man down, the Brumbies pressed home their advantage, and nine minutes later Lealiifano kicked his fifth penalty goal of the night after another scrum infringement.
A 9-3 lead to the Brumbies late in the first half gave the home side the confidence to run the ball more, retaining possession for more than a dozen phases before fullback Robbie Coleman scrambled over the tryline after the halftime siren.
The Bulls declined a penalty shot directly after halftime, and after several phases winger Lionel Mapoe crashed over the line, only to lose the ball in a late tackle by Brumbies winger Henry Speight.
But winger Jurgen Visser scored in the 49th-minute when he finished off a well-worked passage of play from the Bulls.
ACT 23 (Robbie Coleman try; Christian Lealiifano 6 penalties), Bulls 20 (Johannes Engelbrecht, Jurgen Visser tries; Morne Steyn 2 conversions, 2 penalties). HT: 14-3. – Sapa-AP.