The co-hosts, chasing Pakistan's modest 213 all out, were reduced to 59 for three in the 11th over before they recovered to post a six-wicket win in front of a packed house of 47,000 at the Adelaide Oval.
Steve Smith (65) and Shane Watson (64 not out) swung the match around with a fourth-wicket stand of 89 and Glenn Maxwell smashed an unbeaten 44 off 29 balls as Australia won in the 34th over.
But two dropped catches, both off Wahab's bowling, cost Pakistan dearly.
Watson was on four when he hooked a bouncer high to fine-leg where Rahat Ali got under the ball but dropped the catch.
Wahab, who later returned for his second spell in the 29th over, almost removed Maxwell with his second delivery, but Sohail Khan at third man failed to hold the top-edged pull.
"That spell by Wahab was as good as any I have faced in one-day cricket after a long time," Clarke said.
"If that catch off Watson had been taken, who knows what would have happened. This game would have been closer for sure.
"Fast bowling definitely played a part in this game for both teams. If Watson's catch had been taken maybe Pakistan's 213 may have been enough.
"But credit must go to the way we found a way to see through that spell. There was a bit of luck but it also showed Watson's experience."
Clarke said the loss of early wickets did not worry him.
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