Debutant fast-medium bowler Stuart Clark took four for 34, following a first innings haul of five for 55, to complete what he termed a "dream debut" and help Australia hurry to victory with two days to spare.
South Africa were bowled out for 197 in their second innings, leaving Australia with only 95 to win.
"It was a game dominated by the ball and mostly by our bowlers," said Ponting, who said he was mystified by pre-match comments from the South African camp indicating the pitch looked as though it would help spin bowling.
"Some of the things they said leading into the game were real rubbish," said Ponting.
"When we got here on the morning of the game it was pretty apparent it was going to be a seamer's wicket, hence the make-up of our side.
"They had an all-rounder (Andrew Hall) bowling as first change and (spinner) Nicky Boje in their side. All I can say is that we handled conditions a lot better than they did."
Both Ponting and South African captain Graeme Smith said the pitch offered extravagant help to the seamers throughout the match.
Smith paid tribute to the bowling of Clark but said a second-wicket stand of 154 between Matthew Hayden and Ponting had been the main difference between the sides.
Jacques Rudolph's 41 Saturday was the highest score by a South African and the home side managed only one partnership of 50, between Rudolph and Hall.
Smith said there had been some loose shots by his batsmen in the first innings but felt the pitch was the main reason for the low scoring. "Not only did it seam, it was quite two-paced, which made it difficult to score freely."
Smith said he expected conditions would continue to be difficult for batting in the remaining two Tests, in Durban and Johannesburg, because the matches were being played later than usual in a South African season.
Despite the emphatic defeat, which followed a 2-0 loss in a three-match series in Australia earlier this season, Smith insisted his team were becoming more competitive.
"We know Australia are the number one team in the world but the exciting thing for us is we know we are getting closer and closer to beating them."
Clark struck two key blows Saturday morning by dismissing overnight batsmen Jacques Kallis and Ashwell Prince after South Africa resumed at a shaky 70 for three.
He came back in mid-afternoon to take two more wickets and stand on the brink of becoming only the third Australian, after Clarrie Grimmett in 1924/25 and Bob Massie in 1972, to take ten wickets in a match on debut.
Leg-spinner Shane Warne took the final wicket, however, when last man Ntini holed out to long-off.
South Africa's hopes rested largely on Kallis at the start of play. He clipped Brett Lee's third ball of the day confidently to square leg for four.
Clark struck with the third ball of the day's second over when Kallis, on 36, attempted a forcing shot off the back foot and wicketkeeper Adam Gilchrist leapt high and to his right to take an excellent catch.
Clark bowled impeccably, conceding just one run off his first five overs. In his sixth over, bowling around the wicket, the left-handed Prince edged a sharp chance which went for four through the fingertips of Shane Warne at first slip.
Prince did not take advantage of the let-off, however, and was out for 27 off the next ball when he glanced a catch down the leg-side to Gilchrist.
Mark Boucher made only two before he clipped Kasprowicz to midwicket, where Justin Langer took a smart low catch.
Rudolph's dismissal half an hour after lunch signalled a rapid end to South Africa's resistance. Nicky Boje batted aggressively to make 14 off 15 balls with three fours but he was out to the first ball of Clark's second spell of the day, pushing back a return catch.
Clark's final wicket came off the last ball of the same over when he bowled Andre Nel.
Justin Langer and Hayden put on 71 before Makhaya Ntini took three wickets in five balls. Hayden was caught off a mistimed pull.
Three balls later Ntini bowled Langer off an inside edge and with the first ball of his next over he trapped Ponting leg before wicket.
South Africa, first innings, 205
Australia, first innings, 308
South Africa, second innings (overnight 70-3)
Falls: 1-20, 2-20, 3-37, 4-75, 5-92, 6-108, 7-158, 8-179, 9-183
Australia, second innings (target 95)
Falls: 1-71, 2-71, 3-75
Did not bat: A Symonds, A Gilchrist, S Warne, B Lee, M Kasprowicz, S Clark.
Result: Australia won by 7 wickets.
Australia lead a three-match series 1-0.
Remaining matches: Durban, March 24-28; Johannesburg, March 31-April 4.