North End lie fourth bottom in the Championship but they belied their lowly status with a vibrant display and the award of a 60th-minute spot-kick put them on course for a notable upset.
And North End midfielder Darren Carter compounded the misery among home supporters when he bundled the ball into his own net in the 93rd minute following a corner from Croatia midfielder Niko Kranjcar.
Harry Redknapp - whose side are in the quarter-finals for the first time since 2004 - said: "David James is different class and the lad taking the penalty must have stepped up and realised how imposing he is.
"If anyone can make a save it's going to be him because he's that good.
"In the last couple of weeks he's been in great form but he's been like that since he came to the club.
"He's been on another level - absolutely fantastic - and hopefully he can continue in that vein."
Redknapp was forced to admits his side were fortuitous to escape with victory.
"I was thinking 'let's get them back to Fratton Park'," said Redknapp. "But you need a bit of luck and we had that at Bolton a couple of weeks ago and w had it today.
"It was a difficult game at Preston made life difficult. The pitch wasn't great but what Preston had was a willingness and a pace up front, and I thought they were excellent."
Preston boss Alan Irvine could hardly have asked any more of his players and they were desperately unlucky not to earn at least a replay.
The former Everton assistant manager refused to point the finger at Whaley for missing the penalty - awarded after Sylvain Distin fouled Preston defender Billy Jones.
Irvine said: "The first thing he did when he came into the dressing room was apologise.
"But I said he had need to apologise because people miss penalties.
"It's good that he feels that way but we're certainly not going to start pointing the finger.
"We've got some very important games coming up and we're not going to make him feel any worse than he already feels at the moment."
