Clark, who said he had a sleepless night Wednesday not knowing whether or not he would be playing, took five for 55 as South Africa crumbled to 205 all out. Australia were 63 for one at the close.
Clark, 30, took full advantage of overcast conditions and a pitch which offered seam movement as he became the first Australian in more than six years to take five wickets in an innings in his first Test.
He said the Australian team management only decided after the pre-match warm-up that he would play ahead of leg-spinner Stuart MacGill.
"It is a dream come true. Every kid grows up wanting to play for Australia," he said. "It was a bit of a surreal experience."
There was one lapse in Clark's performance - when he dropped a catch at mid-off from number ten batsman Andre Nel off the bowling of Brett Lee.
The incident came soon after he had taken his fifth wicket and he admitted he probably had one eye on the scoreboard.
Fast bowler Lee, the previous Australian to take five wickets on his debut, against India in Melbourne in the Boxing Day Test of 1999, took three for 37 as South Africa crashed back to earth just four days after hammering a world record 438 for nine in a One-day international against Australia.
South African coach Mickey Arthur said it had been a calculated risk to bat first in seam-friendly conditions. He thought his players were a little flat after their efforts Sunday but was confident they could bounce back.
The tall Clark bowled at a brisk pace with a relentless accuracy that would have won the approval of fellow New South Wales player Glenn McGrath, who was not available for the tour because of his wife's illness.
After Michael Kasprowicz made the first breakthrough, bowling AB de Villiers in the tenth over, Clark struck with his ninth ball when he had South African captain Graeme Smith caught behind for 19.
For Smith, who made a century and a 90 in the recent one-day series, it was a continuation of a run of low Test scores against Australia.
He made 155 runs in six innings, with a top score of 39, when South Africa were beaten 2-0 in a three-match series in Australia earlier this season.
Clark plunged the home side into a parlous position, following up the wicket of Smith by dismissing leading batsmen Jacques Kallis and Herschelle Gibbs as South Africa collapsed to 61 for four before lunch.
He continued his spell after the break and had South African wicketkeeper Mark Boucher caught behind before coming back later to trap top-scorer Nicky Boje leg before wicket.
South Africa relied on their lower order batsmen to give some respectability to their innings. All-rounder Andrew Hall, who replaced the injured Shaun Pollock, made 24 batting at number eight while Boje, batting at number nine, scored 31.
The highest partnership was 32 for the last wicket between Andre Nel and Makhaya Ntini, with both tail-enders hitting sixes - Nel off Clark and Ntini off leg-spinner Shane Warne.
Clark has several times been on the fringes of Test selection but a mixture of injuries and loss of form denied him his chance.
He made his One-day international debut in the Super Series against the World XI in October.
Justin Langer was the only Australian batsman to fall before the close as he was given lbw to Nel on 16.
Matthew Hayden became the ninth Australian to reach 7000 Test runs - and to go past Sir Donald Bradman's total of 6996 - when he was on 12.
Earlier Hayden held three catches in the gully to take his total of Test catches to 100 in 80 matches.
South Africa, first innings
Falls: 1-24, 2-42, 3-48, 4-61, 5-76, 6-104, 7-124, 8-148, 9-173
Australia, first innings