Usually regarded as one of the world's best Twenty20 bats, Babar has struggled through this tournament with just one score in double figures.
The Pakistan opener has made 0, 4, 4, 6 and 25 while striking at only 61.90 in a major concern for his team's chances.
But Hayden, who is working with Babar as Pakistan's batting coach, insists there should be no doubting his captain's ability to bounce back.
He pointed to the efforts of Adam Gilchrist in the 2007 ODI World Cup when the wicketkeeper had Australia's lowest average in the tournament of all the regular bats before hitting 149 in the final.
"Babar and Mohammad Rizwan rightly are our No.1 combination opening," Hayden said.
"If you can take your mind back to the 2007 World Cup, when Adam Gilchrist had quite a lean World Cup by his standards.
"And if you remember that last match against Sri Lanka, he went on to score an incredible hundred and realised his potential in that tournament.
"He awakened the world that he was such an incredible batsman in that form of the game."
Hayden warned New Zealand he expected a similar response from Babar at the SCG on Wednesday.
"We all know that in any given career you have significant moments of ups and downs," Hayden said.
"You can't continue to keep punching out 100s and 50s and strike-rates of 140-plus.
"There has to be moments in time when there is a lull. And when there is a lull there is often a storm that follows.
"So look out the rest of the world because I think you are about to see something very special from Babar."
A win for Pakistan would set up a dream final against India, if their rivals topple England in the other semi-final.
New Zealand meanwhile have had their own form issues with captain Kane Williamson, before scores of 40 and 61 leading into the semi-finals.
Williamson scored 85 off 48 in last year's final against Australia and has a history of performing in big games with a crucial 67 against India in the 2019 ODI World Cup semi-final.
"For me it's just focusing on a role," Williamson said.
"We have seen throughout this tournament the variety of conditions and you factor in each opposition and the strengths they have.
"It's about trying to do your bit for the team and trying to make as big of a contribution as you can."
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