The Potters came from a goal behind to win 2-1.
Pulis was quick to praise the supporters who drove the side on with chants of "attack, attack, attack, attack, attack" shortly after the substitutions.
"We must never under-estimate the part our fans play in the way we win games and the way that we do it at the Britannia Stadium," he told the Stoke website. "I thought the substitutions lifted the crowd and they responded by getting right behind the team.
"When we got the equaliser, the belief in the crowd and the level of support was such that you just sensed we could go on and win the game."