Although the hosts made a shaky start in the 'do-or-die' match where a spot in the final against Australia was on the line, Bravo and Pollard led a recover from 21 for four with a fifth-wicket partnership of 156 in 25 overs.
Other useful contributions came from West Indies captain Jason Holder, with a quickfire 40 off 46 balls, and Carlos Brathwaite, with 33 not out.
Right-arm fast bowler Kagiso Rabada was the pick of South Africa's attack, taking 3-31 in his 10 overs while seamer Chris Morris took 3-63. In reply, South Africa lost early wickets as fast-medium bowler Shannon Gabriel and off-spinner Sunil Narine ripped through their top order to leave the Proteas reeling at 65-6 in the 18th over.
Farhaan Behardien (35), Wayne Parnell (28) and tailenders Morne Morkel (32 not out) and Imran Tahir (29) provided some resistance with the bat but South Africa's asking rate kept climbing until they were bowled out for 185 in 46 overs.
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Gabriel finished with figures of 3-17 from five overs and Narine took 3-28 from 10, while Holder was economical with a return of 1-33.
West Indies and Australia will meet in Sunday's final at the same venue.
(Writing by Jahmal Corner in Los Angeles; Editing by John O'Brien)
