Bavuma made a battling, and at times punchy, 171 not out in a South African second innings total of 287 for seven, an overall lead of 356.
It was an emotional moment for Bavuma when he hit Alzarri Joseph over cover for his 14th boundary to reach his hundred, more than seven years after he made his first Test century.
He took off his helmet, leaped in the air and brandished his bat in a salute as a small crowd rose to give him a standing ovation.
The South African captain went on to play with freedom. After reaching three figures off 192 balls, he went on to 171 off 275 deliveries. He hit 20 fours.
Bavuma, 32, made his first hundred in his seventh Test and his eighth Test innings in a high-scoring draw against England at Newlands in Cape Town in January 2016.
Since then he had played in another 48 Tests and batted in 88 more innings without repeating the feat despite hitting 19 half-centuries.
South Africa’s most reliable batsman over the past two years, Bavuma was appointed captain before the first Test against the West Indies – and was out for a ‘pair’.
He came in on Friday with his team in trouble at eight for two.
It was a long struggle as he accumulated a 107-ball half-century while partners struggled and succumbed against good-quality West Indian bowling.
They were 103 for five, a precarious 172 runs ahead, when Bavuma was joined by Wiaan Mulder, one of several South African batsmen yet to prove themselves at top level.
By tea, South Africa had scored only 145 for five off 59 overs but the tempo changed when Mulder hit three fours off Kemar Roach in the second over after the interval.
Mulder made 42 in a 103-run partnership which accelerated further after Bavuma reached his century.
Mulder holed out to deep square leg but by then South Africa were in a position of relative safety. Twenty-one overs between tea and the taking of the second new ball yielded 98 runs for the loss of Mulder’s wicket.
Simon Harmer joined Bavuma in another productive partnership, making 19 while Bavuma scored freely as the pair added 71 for the seventh wicket.
Harmer fell late in the day, leg before to a Jason Holder delivery that shot through low and hit him below the knee roll.
It was the first inkling that the pitch, which has not posed any great problems, may be a different beast in the fourth innings.
South Africa are seeking as big a lead as possible, however, as there is concern about the fitness of Kagiso Rabada, one of only two fast bowlers picked by the hosts.
Rabada bowled superbly in the first innings, taking two for 19 in 12 overs, but did not bowl after tea on the second afternoon and was reportedly suffering from a sore back.
There has been no official confirmation of an injury but Bavuma will be glad to have the extra runs to play with as he attempts to lead South Africa to a 2-0 series win.
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