With no prospect of a result at East London's Buffalo Park, the game was called off an hour before the scheduled close with Border having reached 340 for 8 in their second innings.
The last act of the match was Wiblin going to his century in 139 minutes, off 103 balls and with 14 fours and a six.
Border resumed on 21 without loss and batted solidly all day as the West Indian bowlers toiled without significant success.
The major partnership was the 163 Craig Sugden and Mark Boucher shared for the second wicket. They departed in successive overs, both for 84. Sugden faced 165 balls and hit nine fours and two sixes, while Boucher's innings came off 111 balls with 13 fours and a six.
Wiblin and Pieter Strydom then added 87 for the fourth wicket as Border effectively ended the match as a contest.
They were 206 runs ahead at tea, when a token declaration was expected, but it never came and consequently the game petered out.
Leg-spinner Rawl Lewis wheeled away for 26 overs in claiming 3 for 106, the best of the West Indian bowling figures.
The tourists now travel to Port Elizabeth, where the second Test against South Africa starts on Thursday. The home side have brought in Herschelle Gibbs for Adam Bacher as the only change to their squad for the game at St George's Park. Gibbs is set to open despite having appeared in the middle-order for most of his career.
TOUR MATCH (East London; final day of three): Border 282 for 9 dec (C B Sugden 76, B M White 56; M Dillon 4-56) and 340 for 8 dec (W Wiblin 100no, C B Sugden 84, M V Boucher 84); West Indies 356 (S Chanderpaul 92, P A Wallace 68; P Enslie 4-124). Match drawn.
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