Jayawardene's superbly-paced 115 not out was the cornerstone of Sri Lanka's imposing score of 289 for five against New Zealand in the first semi-final at Sabina Park.
In reply, after a fine opening spell from Lasith Malinga, who took one wicket for five runs in four overs, the spinners sparked a middle-order collapse.
New Zealand lost five wickets for 11 runs in 23 deliveries, with off-spin star Muttiah Muralitharan taking three on his way to four for 31.
Jayawardene said a combination of the captaincy and the influence of Moody, a member of Australia's World Cup winning squads in 1987 and 1999, had been key factors in his growing toughness.
"I have become mentally much stronger the last two years," Jayawardene said after scoring a maiden World Cup hundred in his 23rd tournament appearance.
"The captaincy probably would have helped but Tom definitely has pushed me to the limits.
"He's not happy when I'm cruising. He's not happy with anyone cruising. He has pushed me and I have found out I can push myself as well."
Jayawardene took 48 balls to score his first boundary but accelerated to such an extent he scored three sixes and 10 fours in a 109-ball innings.
"I thought 240 would be a competitive score and anything beyond that was to our advantage," he said after becoming this World Cup's second leading run-scorer behind Matthew Hayden with 529 to the Australian's 580.
"Tillakaratne Dilshan came in and got some quick runs and it released some pressure from me. I knew I could hit a few boundaries and everything fell into place."
Off-spinner Dilshan turned up trumps with the ball too, taking just five deliveries to strike when dismissing key New Zealand batsman Scott Styris for 37.
"I never expected Dilshan to pick up a wicket that early. That was a bonus. Once we got that, Murali also came up and asked can he have a go at the batsmen for a couple of overs and see if he can pick up a couple of wickets because that was a good time to put pressure on New Zealand.
"He picked up two wickets in that extra over, so it worked pretty well."
Jayawardene also paid tribute to Malinga, returning to the side after a three-match injury absence, who has made a major impact upon world cricket with his unique round-arm action.
"The guy has been putting in a lot of effort and he was very upset when he's not been part of the team. I wasn't surprised because he's got a big heart."
Sri Lanka's win was all the more impressive as dynamic opening batsman Sanath Jayasuriya, one of three survivors from the side that won the 1996 World Cup along with Murali and left-arm quick Chaminda Vaas, made just one.
But 22-year-old opener Upul Tharanga, under pressure for his place, responded with a tournament best 73.
"Sanath's been a great cricketer with the way he goes about his game and if he carries on obviously we are at an advantage. But we have taken a lot of pressure off Sanath in the last 12 months," said Jayawardene.
Sri Lanka will now face either double-defending champions Australia or South Africa in Saturday's final in Barbados.
"If you're to win the World Cup, you've got to beat the best. Whoever comes through, we'll be happy to play them."
And Jayawardene also said he hoped his side could emulate the long-term impact of the 1996 team.
"The '96 group changed the course of Sri Lankan cricket completely and those guys cleared the way for us to achieve higher goals."