Goals from Kevin Davies and Johan Elmander in the last ten minutes saved Bolton's blushes and denied York a lucrative replay.
With just seven minutes remaining York looked set to take Bolton back to the Bootham Crescent on January 18, but substitutes Davies and Elmander smashed their efforts home to deny the non-league club.
Bolton's defences were tested as early as the fifth minute when Ashley Chambers charged through, but he failed to take the shot and the opportunity went a begging.
He had the opportunity to make amends two minutes later when he came in from the right, but he shot wide before Rankine sent his effort the wrong side of the post a short while later.
Bolton slowly began to test their visitors with Cohen, Rodrigo and Gary Cahill all having chances, but York stayed strong and the sides went in level at the break.
Davies was brought on for Ivan Klasnic at the start of the second half and he almost had an instant impact only for Chris Carruthers to block his shot.
As Bolton went in search of the winner, Owen Coyle took the opportunity to introduce Elmander for Blake, but it was York that went close a short time later when Neil Barrett's shot towards the bottom-right corner found Adam Bogdan.
Just a minute had passed when Martin Petrov found Davies from the left and he fired his effort into the York goal.
Just five minutes later the lead was doubled when Elmander found the same spot with a brilliant 25-yard strike to end York's hopes of forcing the replay.