Rabada scored 31 and Jansen 16 in an unbeaten partnership of 51 off 50 balls to see South Africa over the line on Sunday and deny Pakistan a dramatic comeback victory after Mohammed Abbas took six wickets as he shredded through the home batting order.
The test had a finish more like that of a Twenty20 match as the tailenders delivered success after South Africa had slumped dramatically before lunch and offered Pakistan the chance to win a test in South Africa for the first time in 18 years.
Rabada, who is ranked second best test bowler, emerged, however, as an unlikely batting hero while Jansen delivered the winning runs with a classy drive to the boundary, amid scenes of delirious celebration.
"Quite an emotional one and a good advert for test cricket. A lot of joy and happiness for us but a bit of a rollercoaster. We did it the hard way but we're glad to be able to get the result," said home captain Temba Bavuma.
It was heartbreaking for Pakistan as Abbas had brought them close with four wickets in a marathon spell of 13 successive overs before lunch as South Africa made heavy work of chasing a modest target of 148.
Abbas, whose overall figures were 6-54 off 19.3 overs, engineered a dramatic collapse when South Africa looked headed for a comfortable victory with 50 runs needed and six wickets in hand.
His haul included the fortunate dismissal of captain Temba Bavuma for 40, who walked after thinking he had edged the ball behind to the wicket keeper but will be ruing not reviewing the decision as the television replays showed it had not touched his bat but rather his pocket on the way through.
Mohammad Abbas' brilliant 6-54 haul for Pakistan was not enough to deny South Africa victory. (AP PHOTO)
Abbas also bowled Aiden Markram and had David Bedingham and Corbin Bosch caught behind -- Bosch going first ball to see South Africa slump from 96-4 to 99-8.
"I'm extremely proud of our efforts but going forward as a team, we need to be more ruthless. We have to seize the moments that test cricket provide," said Pakistan captain Shan Masood.
South Africa have now won six successive tests, starting with success in the West Indies in August and following it with two-test series wins in Bangladesh and then home to Sri Lanka last month.
They moved top of the WTC standings after beating Sri Lanka in Gqeberha but needed to win one of the two-test series against Pakistan to make sure of a place in the final at Lord's in London from June 11-15.
The second test between South Africa and Pakistan is at Newlands in Cape Town, starting on Friday.Â
