The Proteas were confined to the pavilion for the first three hours on Monday and for another 30 minutes later on after rain peppered Port Elizabeth, while they then saw Brathwaite (106) and Samuels (101) stall their push for victory by completing hundreds.
But once Samuels and Brathwaite departed in successive overs, the tourists collapsed, losing a further five wickets for 42 runs to sink to 275-9, still 142 runs behind South Africa???s first-innings total, before the weather intervened once more.
Spinner Imran Tahir (3-108) shone for South Africa, who will now be hoping to polish off West Indies early on day five, make quick runs and then skittle out the Caribbean team again to secure an unassailable 2-0 lead in the three-match series.
Brathwaite and Samuels took their partnership from an overnight 92 at St George???s Park to 176, a record third-wicket stand for West Indies against the Proteas, with the batsmen securing their third and sixth Test centuries respectively.
However, Samuels ??? after facing a short-ball barrage from Morne Morkel, which included a blow on the back of his helmet ??? was snared lbw by Vernon Philander, and Brathwaite???s measured knock came to an end when he edged Morkel to Alviro Petersen at slip.
Shivnarine Chanderpaul (7) and Denesh Ramdin (20) fashioned 27 runs in unison before the latter was hit on the pads by Tahir, and Chanderpaul then came a cropper in peculiar circumstances when Tahir dribbled a googly between his legs and onto his stumps.
Jason Holder (1) feathered the impressive Morkel into AB de Villiers’ mitts; Sulieman Benn (4) took an almighty swipe and clipped Tahir to Petersen; and debutant Kenroy Peters (0) was run out by the missile-armed Dale Steyn as West Indies trudged off sullenly when more rain hit.
The inclement weather has already played havoc in Port Elizabeth, with just six overs possible on day two and a combination of a sodden outfield and bad light causing a postponed start and premature ending to day three.
But that may not prevent South Africa, who walloped Ramdin???s men by an innings and 220 runs in the first Test in Centurion last week, surging to a 10th Test series win in 12 ahead of the final encounter in Cape Town from January 2.
Dean Elgar (121) and Faf du Plessis (103) posted centuries for the hosts in their first innings after they were put into bat by Windies skipper Ramdin, but the most eye-catching knock came from Steyn, who??thumped 58 from 28 balls.
The fast bowler brought up his half century from just 26 deliveries, making it the swiftest fifty at Port Elizabeth and the joint fourth fastest in Test-match history, only behind Misbah-ul-Haq (21 balls), Jacques Kallis (24 balls) and Shane Shillingford (25 balls).