"On paper, they may be the favourites, but we have a superior record in major tournaments."
South Africa go into the quarterfinal as Group B winners with five victories in six matches, while New Zealand finished fourth in Group A with four wins.
But Donald, known in his playing days as 'White Lightning', said past performances counted for little in sudden-death situations.
"The thought that your World Cup will be over if you slip up just once is enough to make everybody nervous," he said. "The team that wins will be the one that handles pressure the best."
Donald knows better than most what pressure in a crunch match can do.
He was involved in a disastrous run-out with Lance Kluesner in the 1999 World Cup semifinal when South Africa needed just one run to win, allowing Australia to tie the game and make final on superior run-rate.
It was yet another instance of South Africa succumbing to their trademark knock-out blues.
The Proteas have crashed out three times in World Cup semifinals, once in the quarterfinal and another time in the first round, earning them the unwanted tag of cricket's perennial chokers.
The six-run loss to England in this tournament, chasing a modest 172, was another example of South Africa's brain freeze, even though the demons were exorcised by surpassing India's 296 with three wickets in hand.World Cup 2011
Leading all-rounder Jacques Kallis was confident the past will not return to haunt South Africa.
"We have to just keep doing the things that we did in the group stage, where we played some unbelievable cricket," he said. "There is no reason to change anything."
Kallis admitted New Zealand will not be easy to beat despite South Africa starting out as firm favourites.
"New Zealand are a dangerous side that on their day can beat anyone," he said. "They bat deep and have plenty of all-rounders.
"The game won't be over even if we get early wickets and it's crucial that we stay on top of our game for 300 balls and ensure that we pounce at the slightest sign of weakness."
New Zealand's four league wins included a sensational 110-run victory over Pakistan in Pallekele following a Ross Taylor blitz on his 27th birthday.
Taylor smashed an unbeaten 131 off 124 balls with eight boundaries and seven sixes as the Kiwis hammered 100 runs in the last five overs.
The Black Caps will be boosted by the return of influential skipper Daniel Vettori, who missed the last two matches with a knee injury.
The winner on Friday will face either Sri Lanka or England in the semi-finals.