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.
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 bowler having New Zealand captain Stephen Fleming lbw for one.
It was surprising when he was taken off by Jayawardene after a superbly accurate opening spell of one wicket for five runs in four overs.
Left-arm quick Chaminda Vaas made it 32 for two in the 11th over when Ross Taylor tried to hit across the line and was lbw for nine.
Scott Styris, fifth in the list of tournament run-scorers, counter-attacked by driving Dilhara Fernando and Muralitharan for sixes.
After two overs for 14 runs, Murali was replaced by fellow spinner Tillakaratne Dilshan.
It took just five balls for Dilshan to strike, Styris on 37 chipping to Jayawardene at mid-wicket who gleefully held a catch above his head.
That was the start of a collapse that saw Sri Lanka's spinners taking five wickets for 11 runs in 23 balls to all but seal victory as New Zealand slumped to 116 for seven.
Murali held a brilliant lunging one-handed catch to dismiss all-rounder Jacob Oram off his own bowling.
Next ball Brendon McCullum's top-edged sweep was athletically caught by a diving Chamara Silva, running round from square leg to leave Murali on a hat-trick at the start of his next over.
But before then opener Peter Fulton, who top-scored with 46, chipped left-arm spinner Sanath Jayasuriya, one of three survivors along with Vaas and Murali from the 1996 team, to Silva at mid-on.
Daniel Vettori survived the hat-trick but was then plumb lbw to Murali's 'doosra' for nought.
And not even a few hard hits from Craig McMillan, batting at seven and with a runner after being off the field with a stomach muscle injury, were going to change the outcome.
A last wicket stand of 59 delayed proceedings before Jeetan Patel (34) was last man out, holing out off Dilshan.
Earlier, Sri Lanka opener Upul Tharanga struck a tournament best 73 as his team recovered well after Jayasuriya fell for one.
Crucially, Sri Lanka lost just one wicket to strike bowler Shane Bond, returning after missing Friday's 215-run thrashing by Australia with a stomach illness.
The quick conceded 59 runs and he dropped Jayawardene, who led a charge that saw 102 runs scored off the last 10 overs.
At the halfway stage, Sri Lanka had been well-placed for a big total at 111 for three.
But next ball they lost Tharanga when the left-hander was bowled sweeping by Vettori for a 73 made off 74 balls with one six and nine fours.
Jayawardene subsequently drove Oram, fit again after a heel injury, over his head for six.
His sweep against off-spinner Patel was dropped by Bond on the deep backward square leg boundary, the ball bouncing out of the fieldsman's hands before hitting the rope for a six.
Jayawardene went to his hundred, off 104 balls, with a superb late cut boundary against Oram before pulling Bond for six as the bowler's last over went for 17.