The Potters' keeper stopped Christian Doidge's shot in the first half and then denied centre half Mark Beevers late on.
In contrast, Butland's opposite number, Ben Alnwick, was rarely troubled as Stoke failed to score for a second successive game.
Wanderers' latest point lifted Phil Parkinson's side out of the bottom three ahead of a New Year's Day trip to Hull.
Both teams made two changes to their starting line-ups from the Boxing Day games against Rotherham and Birmingham.
Wanderers' 2-1 win over the Millers was their first in 14 games though they started against Stoke without match winner Gary O'Neil through injury.
City, who dropped Martina and Berahino to the bench, were hoping to return to winning ways after a 2-0 reverse at Birmingham.
Rowett's men started brightly, dominating possession against a Wanderers side giving a first start since October 6 to left back Jonathan Grounds.
One-time Bolton loanee, Benik Afobe, crossed from the right but James McLean's header was well saved by Alnwick.
Sam Clucas then mis-hit a shot after Tom Ince worked an opening on the Wanderers' left.
For all their possession, however, Stoke's passing lacked penetration and direction making it easy for Bolton to defend their penalty area.
And it was the home side who fashioned the better chances as the half drew to a close.
Twice, Josh Vela – O'Neil's replacement – tried his luck but each time his right foot shots lacked power.
And it needed a fine save by Butland too keep Stoke on terms. Striker Doidge's right-foot effort was heading towards the top corner until Butland diverted it away for a corner.
Bolton started the second half on the front foot with the impressive Joe Williams chipping an angled shot onto the roof of Butland's net.
Doidge then curled a right-foot shot goalwards but didn't get the bend on the ball he had hoped for.
Clayton Donaldson's yellow card and follow-up foul signalled the end of his afternoon with Josh Magennis replacing the veteran striker.
City boss Gary Rowett eventually made his own changes taking off Tom Ince and Sam Clucas and introducing Peter Etebo and Tyrese Campbell.
With 10 minutes left, Stoke made their final switch with Afobe going off and Peter Crouch coming on.
But it was Bolton who again went closest to breaking the deadlock. And again it was Butland who came to City's rescue.
Magennis crossed to the back post where Beevers rose highest to head goalwards. But with the ball heading to the bottom corner, Butland made a brilliant save.
And it wasn't until stoppage time when Stoke managed one final chance with substitute Campbell shooting wide from distance.