Manager Simon Grayson says Preston were dragged to by the knowledge Manchester United awaited in the fifth round.
North End were 1-0 down with 27 minutes to play, but Paul Gallagher's brace and a Paul Huntington header set up a
It also ended a seven-game winless run.
"We showed a lot of character. We've really struggled for a month but, as I said it could, that Manchester United game galvanised us," said Grayson.
|FA Cup fifth-round draw|
|Crystal Palace v Liverpool or Bolton||Arsenal v Middlesbrough|
|Aston Villa v Leicester City||West Bromwich Albion v West Ham|
|Bradford City v Sunderland||Blackburn Rovers v Stoke City|
|Derby County v Reading||Preston v Manchester United|
He told BBC Radio Lancashire: "Both teams knew what was at stake because Manchester United are one of the biggest teams around.
"We've have some bad results but I told the players at half-time that they needed to believe and they did."
Preston's recent bad run has seen them drop off the pace in League One as they now sit fourth, eight points adrift of the automatic promotion places.
On Saturday they were and Grayson made six changes to his starting XI for the FA Cup fourth-round replay at Bramall Lane.
"As a manager you make decisions. Sometimes it works, sometimes it doesn't," he continued. "The players were fully committed, a constant threat and fully deserved to win.
"Now we can use this to chase down the top two in the league and get what is our top priority for the season."