South Africa lost three early wickets and at one stage were 33-3 in reply to Zimbabwe's 201-7. But Dippenaar, in his 100th One-day international, helped by a career-best 60 from Jean-Paul Duminy, guided the hosts to a comfortable win.
Vusi Sibanda top-scored for Zimbabwe with eight fours in his 51.
Left-hander Duminy, who was overlooked for next month's Champions Trophy squad, batted with confidence as he and Dippenaar shared a fourth-wicket stand of 121.
The partnership was finally brought to an end when 22-year-old Duminy charged down the pitch to off-spinner Stuart Matsikenyeri and was stumped.
Ed Rainsford was the best of the Zimbabwe bowlers, taking two for 29 off 10 overs.
Zimbabwe won the toss and Sibanda batted well after a shaky start with his 51 off 78 balls helping them to 137-2 after 33 overs.
He was dismissed when mis-timing an attempted pull to mid-off three balls after passing fifty for the sixth time in an ODI.
His effort was backed up by Justice Chibhabha (37) and Hamilton Masakadza (32).
Masakadza was caught at cover off the hostile Jacques Kallis, Chibhabha got a leading edge while trying to work the ball on the on-side as Zimbabwe began to struggle.
Shaun Pollock, Makhaya Ntini (1-29) and Kallis (2-18) in his first ODI as captain bowled tightly to tie Zimbabwe down but Elton Chigumbura produced an entertaining late cameo to hit 26 off 31 balls and lift the score to over 200