The Cheetahs were unlucky to go home without the victory, after leading for most of the match and by as much as 13 points in the second half.
But the Brumbies held their nerve, including opting for an easy penalty with less than five minutes left to narrow the gap to two rather than running the ball in search of the lead.
It paid dividends in the end, after a frantic final three minutes when Brumbies captain Ben Mowen dropped the ball which was called backwards and the Cheetahs then knocked forward.
Cheetahs inside centre Philip Snyman then intercepted a ball and made a break, but he opted for a speculative pass which ended in the arms of Pat McCabe who kept the Brumbies' chances alive.
The Brumbies then drew the penalty they needed to win the game, and Lealiifano held his nerve when it counted.
The result did not do the Cheetahs justice.
They started well with a third-minute penalty and then showed their intentions by throwing the ball around in perfect conditions for rugby.
After Johan Goosen made a meal of a field goal attempt to try pinch an early break the Brumbies hit back, with Henry Speight scoring out wide in the ninth minute after Nic White picked up a loose ball and sprinted 30 metres through traffic.
The Brumbies were camped in their attacking half for most of the opening half but were unable to capitalise, before the Cheetahs scored in the 19th minute in their first foray forward for a good 15 minutes.
Cheetahs' prop Coenie Oosthuizen was the unlikely playmaker, running off the back of a lineout and putting Willie Le Roux through a hole and he stepped his way through the Brumbies' defence and ran 30 metres to score untouched.
Lealiifano then slotted a difficult penalty on the right touchline to level the scores at 10 apiece before they gifted Goosen an easy penalty on the stroke of half time and he put his side back in front into the break.
The Cheetahs struck a minute into the second half, with Le Roux at his evasive best on the left wing, stepping inside and putting Tewis de Bruyn over out wide, with Goosen converting from the touchline.
Ben Hand gifted Goosen another simple penalty to extend the Cheetahs' lead to 13 with just over half an hour left.
The Brumbies then hit back minutes later. After repeated phases deep in their attacking half they swung the ball out to the right with Matt Toomua putting returning Wallaby McCabe over.
Lealiifano missed the conversion to keep the lead at eight.
Goosen then had a 62-metre wind-assisted penalty attempt, but fell five metres short.
Brumbies flanker Scott Fardy dived over in the 61st minute, but was pulled back for offside.
The Brumbies retained possession and after repeated infringements from the Cheetahs Lealiifano slotted a penalty to narrow the gap to one try.
They came home strongly with the Cheetahs' ill discipline proving costly after such a valiant effort for most of the afternoon.