Pakistan were bowled out for 235 in their second innings, having managed 156 in their first in reply to South Africa's 409.
The win, completed in three days, made Graeme Smith the first captain to claim 50 test wins.
"It has been a very special summer at home with some incredible milestones for myself and the team," Smith told reporters. "To be able to achieve something today in winning 50 tests with a special group of cricketers is something that will stay with me for the rest of my life."
Abbott, who had come in for the injured Jacques Kallis, was the pick of the South African seamers on a helpful wicket, recording match figures of nine for 68.
The 25-year-old took the scalps of Imran Farhat (43) and Ehsan Adil (12) to add to his seven wickets from the first innings.
"My knowledge of Kyle was limited going into the test match so it was fantastic to see him bowl as well as he did," Smith said. "He bowled at a good, solid pace, hit the deck hard, got the ball in the right areas. He asked a lot of questions."
Starting the day on 14 for one, Pakistan showed some fighting spirit losing only Younus Khan (11), who played a thick edge off Dale Steyn to Smith at first slip, in the morning session.
The tourists began to implode after lunch. Azhar Ali (27) and Farhat put on 54 for the third wicket before the former ran himself out in calamitous fashion.
Farhat worked the ball to fine leg and after running one, Ali turned for a second at the wicketkeeper's end. He was always struggling against the bullet throw of Steyn from the boundary and in the end was well short.
Pakistan lost two more wickets with the score on 107.
Abbott picked up his eighth of the match when Farhat (43) slashed at a wide delivery and was caught by wicketkeeper AB de Villiers.
Captain Misbah-ul-Haq (5) became Rory Kleinveldt's first wicket of the game when he got a thin edge to a ball. Kleinveldt took a second when Asad Shafiq (6) scooped a delivery to Vernon Philander at mid-off.
Saeed Ajmal (31) and Sarfraz Ahmed put on 69 for the seventh wicket, but the former was trapped lbw by Steyn to end the resistance.
Sarfraz (40) followed soon afterwards when he top-edged Steyn to Dean Elgar at third man and Ehsan Adil tried to pull Abbott but only succeeded in ballooning the ball to Kleinveldt at mid-on.
The final pair of Mohammad Irfan (6 not out) and Rahat Ali (22) hung around for another 33 runs before Rahat was lbw to Robin Peterson to end the match.
South Africa won the first test in Johannesburg by 211 runs and completed a four-wicket victory in the second in Cape Town.
"This is the best team I have played in as a South African cricketer, we have all our bases covered," Smith said. "Part of that is the maturity and professionalism with which they approach every match. If you are even 10 percent off in your game it can affect the result, but the guys gave it everything again."
Pakistan captain Misbah said his team lacked consistency.
"Full credit to the South Africans for the way they played in this series, their batting, bowling and fielding was better," Misbah said.
"We had an opportunity to win the second test in Cape Town with two hundreds and 10 wickets for Saeed Ajmal, but a batting collapse hurt us there. It has been the story of our series."