Leali'ifano missed two of his first three shots at goal, then landed three in succession as the Brumbies relied on penalties to beat the Bloemfontein-based Cheetahs, who were appearing in a playoff match for the first time. Scrumhalf Nic White also kicked a long-range penalty for the Brumbies, who won the most-recent of their two Super Rugby titles in 2004.
The Christchurch-based Crusaders will now play the Hamilton-based Chiefs, the defending champion, in an all-New Zealand semifinal after their 38-9 win over the Queensland Reds on Saturday.
Sunday's match at Canberra didn't come close to matching the high standard set by the seven-time champion Crusaders in their four tries to nil win over the Reds the day before.
The Cheetahs looked stage-struck for the first 15 minutes of the match but came alive when center Johann Sadie scored their first try in the 16th minute, giving them a 5-3 lead.
The lead changed hands three times before White's long-distance penalty in the 47th minute put the Brumbies ahead 9-8. They then extended that lead to 15-8 with penalties to Leali'ifano in the 58th and 66th minutes.
The Cheetahs refused to let the match get away from them and attacked relentlessly through the last five minutes, remaining competitive though the tide of penalties from New Zealand referee Glen Jackson ran strongly against them.
They had the chance of several kicks at goal in the last five minutes but rejected that option as they sought the converted try that would take the match to extra time. With time up on the clock at Canberra Stadium, Pretorius engineered the try to Benjamin that gave Smit the chance to tie the scores.
His dying-seconds kick missed by inches and the Cheetahs' longest season, their first that extended to the playoffs, ended in muted disappointment.
Brumbies captain Ben Mowen watched in trepidation as Smit's last kick rose towards the posts.
"You always worry when a South African guy's having a kick at goal because they're usually dead on the money," Mowen said. "But, fortunately for us, it went our way there.
"I thought there were moments throughout that game when we played some really good footy. We spoke in the dressing room about being enthusiastic, we spoke about out-willing them in those moments and I thought for the majority of the game we did that."
The Brumbies, who topped the Australian conference and finished third overall at the end of the regular season, played a generally conservative and unimaginative match on Sunday. They kicked for field position and waited for the penalties that inevitably went against the Cheetahs at the fiercely contested breakdown.
"That's an area of strength for us without a doubt, the breakdown," Mowen said. "That was a good effort but we're going to build now and try to run all the way through.
"We're pretty comfortable with the things we've been working on but we've just got to make sure we execute them under game pressure."
The Cheetahs competed well after their initial hesitation and played some of the match's most attractive rugby. Their two tries to none advantage might have been enough to win most matches but they were finally denied by missed goalkicks.
"Obviously we're really disappointed to lose tonight," captain Adriaan Strauss said. "But I'm still proud of the guys.
"We had a much better season this year and that's something we can definitely build on for the future.
"I was very confident in Riaan (to kick the final goal). I thought he had a great kick and I thought it was over but that was unfortunate for us tonight."
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Brumbies 15 (Christian Leali'ifano 4 penalties; Nic White penalty), Cheetahs 13 (Johann Sadie, Ryno Benjamin tries; Riaan Smit penalty). HT: 6-5.
