The tourists went through the final session at St George's Park, brought to an early finish by bad light, without losing a wicket as Brathwaite continued his excellent 2014 unbeaten on 65.
He has put on 92 for the third wicket with the more aggressive Samuels (60) after West Indies had been rocked by two wickets in as many balls just before the tea break.
They have moved the side closer to South Africa’s first innings score of 417 for eight declared and will be confident of getting the additional 71 runs needed to avoid the follow-on.
Right-hander Brathwaite, 22, has scored 660 test runs this year at an average of 82.50 to showcase his rich potential.
"We've got to stay patient with this partnership, but once we get (number five) Shivnarine Chanderpaul out we know we can respectfully race through them," Proteas bowling coach Allan Donald told reporters.
"We knew the West Indies would come here and front up, and this pitch is probably tailor-made for a guy like Chanderpaul where he will just grind away."
Morne Morkel was the pick of the South African bowlers as he dismissed Devon Smith (22) and Leon Johnson (0) in successive balls with the West Indies score on 55.
After striking Smith a sickening blow on the helmet, Morkel claimed his wicket -- caught at first slip by Hashim Amla, while Johnson flashed at a ball that showed a hint of reverse-swing and was snapped up by Faf du Plessis at third slip for a golden duck.
"We as batters know where we score runs, if we spend the required time out there we will score the runs," touring captain Denesh Ramdin said.
"We will back ourselves and be as positive as we can and get as close to their total as possible."
Earlier, Dale Steyn bludgeoned his second test 50, and the fastest ever in Port Elizabeth, off 26 balls as he led the Proteas quickly past 400.
The world’s best fast bowler was eventually dismissed two balls later for 58 in a sparkling innings that included five huge sixes.
South Africa won the first test in Pretoria by an innings and 220 runs, with the third and final match to start in Cape Town on Friday.
(Editing by Pritha Sarkar)
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