West Indies face record target 444 as Taylor posts New Zealand best 17th ton. They were 30-2 at stumps on day 3.
Stirling steered Ireland to a 2-1 series defeat of Afghanistan with a five-wicket win in the final ODI in Sharjah on Sunday.
India were reduced to 29 for 7 in Dharamsala, and then dismissed for 112, as the visitors took a 1-0 lead in the ODI series.
Tim and Trent adventures included one key partnership, four wickets and two spectacular catches, which left West Indies trailing by 158 runs at stumps.
Rohit will lead home side, while visiting team will have a new captain in Thisara Perera.
Scotland claim runner-up position; Hong Kong finish third and PNG qualify fourth.
West Indies late charge unravels New Zealand. At stumps, the host were 286 for seven.
West Indies are up against it to level the series, with the hosts high on confidence Southee set to return.
Ireland square their one-day series against Afghanistan and set up decider on Sunday by earning a superb 51-run win in Sharjah.
Marsh, Stoneman, de Grandhomme, Blundell and Brathwaite others to move up.