Restricted to a meagre 152 for seven in their 50 overs, West Indies were unable to prevent the tourists from coasting to a revised target of 124 in just 26.4 overs and taking a 2-0 lead in the five-match series.
However, Dippenaar then shared in an unbroken stand of 106 for the third wicket with Herschelle Gibbs [ Images ] (44 not out) to guide South Africa home with 38 balls to spare.
Dippenaar was named man of the match for his 78-ball 60 while Gibbs smashed a four and two sixes to add a touch of gloss to the triumph.
South Africa won the series opener at the same venue on Saturday by eight wickets, chasing a victory target of 254.
The home team, who lost the toss, slumped to 67 for six in the 29th over before wicket-keeper Courtney Browne gave the innings a measure of respectability with six fours in his 59-ball 40 not out.
West Indies began poorly with dangerman Chris Gayle [ Images ] bowled for 11 by a perfect yorker from Makhaya Ntini [ Images ] and the out-of-form Wavell Hinds snapped up at slip by South Africa captain Smith off Shaun Pollock [ Images ] for just three.
Dwayne Bravo [ Images ], promoted to number six, ground out 14 runs from 42 balls before a bizarre but brilliant stumping ended his resistance.
The batsman's back foot was six inches behind the popping crease when wicket keeper Mark Boucher [ Images ] removed the bails against medium pacer Justin Kemp but television replays showed clearly his foot was, fractionally, in the air.
Captain Shivnarine Chanderpaul [ Images ] eked out 36 from 95 balls in a bid to give the innings some solidity before he chopped a Langeveldt delivery on to his leg stump.
Although Pollock, with two for 28, and Langeveldt, with two for 33, were the most successful bowlers, fellow paceman Andre Nel [ Images ] applied a stranglehold on the West Indies batsmen, conceding just eight runs in his first eight overs.
The third game in the series will be played in Barbados on Wednesday.
West Indies 1st innings
C. Gayle b Ntini 11
W. Hinds c Smith b Pollock 3
R. Sarwan b Langeveldt 19
B. Lara c Smith b Pollock 0
S. Chanderpaul b Langeveldt 36
D. Bravo st Boucher b Kemp 14
D. Smith c Pollock b Kallis 0
C. Browne not out 46
I. Bradshaw not out 17
Extras (b-1 lb-1 nb-2 w-2) 6
Total (for 7 wickets, 50 overs) 152
Fall of wickets: 1-13 2-29 3-30 4-40 5-66 5-66 6-67 7-103
Did not bat: D. Powell, C. Collymore
Pollock 10 - 2 - 28 - 2 (nb-2)
Ntini 10 - 2 - 33 - 1
Langeveldt 10 - 0 - 33 - 2 (w-2)
Nel 10 - 4 - 26 - 0
Kallis 5 - 0 - 14 - 1
Smith 1 - 0 - 7 - 0
Kemp 4 - 1 - 9 - 1
South Africa 1st innings (D/L Target: 124 off 33)
G. Smith c Lara b Bradshaw 6
B. Dippenaar not out 60
J. Kallis c Dw. Smith b Bradshaw 7
H. Gibbs not out 44
Extras (lb-1 nb-1 w-5) 7
Total (for 2 wickets, 26.4 overs) 124
Fall of wickets: 1-7, 2-18
Did not bat: S. Pollock, J. Ontong, J. Kemp, M. Boucher, C. Langeveldt, A. Nel, M. Ntini
Powell 7 - 0 - 34 - 0 (nb-1 w-3)
Bradshaw 6 - 0 - 16 - 2 (w-1)
Bravo 3 - 0 - 21 - 0
Collymore 7 - 0 - 35 - 0 (w-1)
Dw. Smith 2 - 0 - 7 - 0
W. Hinds 1.4 - 0 - 10 - 0
Result: South Africa won by 8 wickets (D/L Method)