Jayawardene's 115 not out was the centrepiece of an imposing total of 289 for five and showed the value of a well-paced innings after he'd taken 48 balls to score his first boundary.
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Dropped on 70, in all he faced 109 balls with three sixes and 10 fours in his first century in 23 World Cup matches.
In reply, Sri Lanka bowled out the Black Caps for 208 with more than eight overs to spare, off-spinner Muttiah Muralitharan taking four for 31, including a spell of three wickets in six balls.
Sri Lanka, through to their second final, will now play the winners of Wednesday's match in St Lucia between holders Australia and South Africa in Saturday's climax in Barbados.
This defeat meant New Zealand had lost all five of their World Cup semi-finals.
Jayawardene, who'd won the toss under blue skies, saw Sri Lanka take the field in overcast conditions.
Lasith Malinga, having missed three games with an ankle injury, needed just three balls to take a wicket, the slingshot fast bowl