Chasing an imposing 231-run target to win in 31 overs in the rain-curtailed match, West Indies were 190 for six in 26.1 overs when the heavens opened up once again to bring an early end to the decisive game at Sophia Gardens.
Had Pollard not got out after scoring a 23-ball 28, the par for the West Indies would have been 187 for five under the D/L method.
West Indies needed 41 runs off 4.5 overs when play was called off and at that stage, they were required to have scored 193 for six under D/L method.
Darren Sammy and skipper Dwayne Bravo were left stranded at the crease as the on-field umpires decided to call off the match after brief discussion.
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South Africa ended their league engagements with three points from as many matches while West Indies also finished with the same margin but the Proteas advanced to the knockout stage on account of better net run-rate.
West Indies lost opener Johnson Charles (16) early into their run chase as he was caught by wicketkeeper AB de Villiers at short third man off Dale Steyn.
Chris Morris got the prized-wicket of danger-man Chris Gayle in the 12th over just when the big-bodied Jamaican looked like opening up after hitting a few boundaries.
Gayle scored 27-ball 36 with the help of five fours and a straight six down the wicket before curtains were drawn on his short cameo.
West Indies slipped further into misery when they lost the important wicket of Devon Smith (30), trapped leg before by left-arm spinner Robin Peterson, just before the rain halted the proceedings in the 15th over for a brief period.