Kallis took five for 41 in 8.4 overs which included a vital two over spell late in the game at Newlands which brought him the important wickets of Inzamam-ul-Haq and Abdul Razzaq.
Dippenaar shared a 134 run fourth wicket partnership with Jonty Rhodes to steer the South Africans to 265 for eight from 50 overs after winning the toss and batting.
In reply, Pakistan were bowled out for 231 in 47.4 overs after a superb 108 run fifth wicket stand between Inzamam and Younis Khan threatened to take them to an unlikely win before Kallis captured the vital wicket of Inzamam.
He was caught at midwicket by Shaun Pollock for 63, scored off 80 balls and three overs later Younis was spectacularly run out for 72 to end the match as a contest, although some lusty hitting by Shahid Afridi in the final five overs gave the South Africans some cause for concern.
Earlier, Dippenaar and Rhodes came together with the score at 61 for three in the 16th over at a stage when it looked like South Africa would struggle to score 220.
EARLY WICKETS
Rhodes scored 81 by playing with his usual urgency to help Dippenaar emerge from his shell after Herschelle Gibbs, Gary Kirsten and Kallis fell cheaply.
Rhodes's enjoyable innings ended in typical fashion when he was bowled as he tried to reverse sweep off-spinner Saqlain Mushtaq, only to be deceived by the flight and turn. His runs came off 95 balls and included eight fours.
Dippenaar, who scored his runs off 126 balls with seven fours, played with circumspection early on having come to the crease in the first over with the dismissal of Gibbs for a duck, caught at slip by Younis off the bowling of Waqar Younis.
Kallis, who failed to deliver with the bat in the series, came good with the ball and after an initial spell of one for 28 in six overs returned to take four wickets.
Pakistan were required to score at nearly five and a half an over to reach the target but were soon reeling at two for two in the second over after Salim Elahi and Faisal Iqbal were both dismissed without scoring.
Kamran Akmal was caught by Kirsten off right-arm quick Monde Zondeki for 15 which brought Inzamam and Younis together.
Their fine efforts were undone by the rest of the batting which failed to supply the necessary support in the face of a big total and will have left the Pakistanis with some question marks about the squad ahead of the World Cup which starts in February.