Bulls centre JJ Engelbrecht had scored a 78th-minute try, which was converted by Morne Steyn to give the South Africans hope of a draw before Lealiifano slotted the long-range penalty after the Bulls had been penalised from the kickoff.
The Brumbies had earlier taken advantage of Morne Mellet being yellow-carded by referee Jonathon White for constantly collapsing the scrum, to stymie the visitors' second half momentum and slot two penalties.
VIDEO: Brumbies v Bulls, highlights
The victory moved them to 27 points on the table.
Last year's champions the Chiefs had earlier moved to 25 points after they had beaten the Blues 23-16 in Tauranga.
Much of the first half was played between the 22-metre areas as both sides seemed content to kick for territory and attempt to work off errors inside the opposition half.
The Brumbies forwards surprisingly outmuscled the bigger Bulls pack, allowing their team to make better use of the field position.
Brumbies scrumhalf Nic White missed two long-range penalties while inside centre Lealiifano slotted three closer to the posts to give the home side a 9-3 lead. Bulls flyhalf Steyn had slotted a 20th-minute penalty as half time approached.
The Brumbies forwards then began a rolling maul and a series of pick-and-gos to give their side some momentum before fullback Robbie Coleman ran a superb angle from behind the point of attack and scored the only try of the first half, two minutes after the halftime hooter had sounded.
The match opened up more in the second half with Bulls winger Lionel Mapoe losing the ball over the line in the tackle, before Jurgen Visser finished off a well-worked backline move to score his first Super Rugby try in the 48th minute.
Steyn added the conversion then slotted his second penalty of the match four minutes later that brought the visitors to 14-13 and sensing the momentum had shifted.
Bulls loosehead prop Mellett, however, was sinbinned for constantly collapsing the scrum with 17 minutes remaining, which allowed the Brumbies to add two further Lealiifano penalties.
Engelbrecht then finished a counter-attacking movement that had swept from halfway after the Bulls had turned the ball over and Steyn converted from wide out to look like the visitors had earned two points for the draw.
Scorers:
Brumbies – Try: Robbie Coleman. Penalties: Lealiifano (6).
Vodacom Bulls – Try: Jurgens Visser, JJ Engelbrecht. Conversions: Morne Steyn (2). Penalties: Steyn (2).
Teams:
Brumbies:
15 Robbie Coleman, 14 Henry Speight, 13 Tevita
Kuridrani, 12 Christian Lealiifano, 11 Joe Tomane, 10 Matt Toomua, 9 Nic
White, 8 Ben Mowen (captain), 7 George Smith, 6 Peter Kimlin, 5 Etienne
Oosthuizen, 4 Scott Fardy, 3 Dan Palmer, 2 Stephen Moore, 1 Ben
Alexander
Substitutes: 16 Siliva Siliva, 17 Scott Sio, 18 Fotu Auelua, 19 Colby Faingaa, 20 Ian Prior, 21 Andrew Smith, 22 Clyde Rathbone
Bulls:
15
Zane Kirchner, 14 Lionel Mapoe, 13 JJ Engelbrecht, 12 Jan Serfontein,
11 Jürgen Visser, 10 Morne Steyn, 9 Jano Vermaak, 8 Pierre Spies
(captain), 7 Dewald Potgieter, 6 Deon Stegmann, 5 Juandrè Kruger, 4 Paul
Willemse, 3 Werner Kruger, 2 Chiliboy Ralepelle, 1 Morne Mellett
Substitutes:
16 Willie Wepener, 17 Frik Kirsten, 18 Wilhelm Steenkamp, 19 Arno
Botha, 20 Ruan Snyman, 21 Louis Fouche, 22 Francois Venter