Australia was 70-1 at lunch after West Indies captain Jason Holder won the toss and elected to bowl after a delay of an hour due to rain.
Warner looked dangerous once the players eventually took the field, stroking five boundaries in the first three overs before skying a short-pitched Taylor delivery to Marlon Samuels at extra-cover for 23 off just 12 balls.
Joe Burns (27) and fit-again Usman Khawaja (18) continued more sedately to share an unbeaten 41-run second-wicket partnership to the lunch break.
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