Defending a formidable total of 343 for four, the leg-spinner feasted on an inept Caribbean batting effort with outstanding figures of seven for 45 off nine overs, the best-ever returns by a South African bowler in the history of ODI cricket.
Along the way, Tahir, in his 58th match, surpassed the record of Morne Morkel as the fastest South African to 100 ODI wickets in terms of matches played.
Earlier, Hashim Amla's 23rd ODI hundred highlighted a domineering batting effort from the Proteas after they were put in by home captain Jason Holder.
Tahir and Tabraiz Shamsi (two for 41) then extinguished the West Indian reply after a bright opening start, Tahir's record harvest including three in one over as the hosts were dismissed for 204 off 38 overs.
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Tahir and Shamsi, in just his second match, effected the breakthrough after the rousing start of 69 in less than ten overs by openers Johnson Charles (49) and Andre Fletcher (21).
By virtue of the margin of their victory, AB de Villiers' team moves to the top of the standings on 10 points, one ahead of Australia and two more than the West Indies.
Competition shifts to Barbados for the final three preliminary matches, beginning with South Africa versus Australia on June 19 at Kensington Oval, ahead of the final at the same venue a week later.
Amla's effortless innings of 110, which came off 99 deliveries and included 13 boundaries, set the Proteas on their way to the formidable total in partnership with Quinton de Kock.
However it was Faf du Plessis who stole the show over the
final overs of the innings, blazing an unbeaten 73 off just 50 balls in a hurricane knock decorated with six fours and two sixes.
De Villiers, whose dismissal on Saturday triggered the collapse that paved the way for an unexpected Australian victory, contributed 27 to the effort.
"We just need to pick ourselves up after this performance," said a dejected Holder after the match. "We are still very much in the competition and need to put in the hard work before the next match.