The Potters were denied a winning start to their Europa League Group E campaign by Ognjen Vukojevic's close-range finish in the 91st minute at the Valeriy Lobanovskiy Stadium.
The Ukrainian hosts had dominated possession in the first half and should have gone ahead midway through when Andriy Yarmolenko blazed wide with the goal at his mercy - the best of a host of chances they created.
Having weathered the storm, Stoke took the lead 10 minutes into the second period when Cameron Jerome netted on his debut, but after Oleksandr Aliev had hit the bar for Dynamo, Vukojevic intervened at the death, stabbing in Yarmolenko's cross to level the match.
Pulis, whose team have kept six clean sheets already this term, was disappointed they could not hang on for the victory, but was pleased overall with a result which extended their unbeaten run to nine games.
"I am absolutely delighted with the players," Pulis said.
"Obviously we are pig sick that we have conceded late on because it would have been a great result for us, but it is still a very good point.
"Every time someone scores late against you it takes the opportunity of getting three points away and it is disappointing.
"But if you look at the overall picture, to come here and perform the way we have... for some of the players, that is their first 90 minutes this season.
"It is an outstanding performance and achievement from the group we had."
Several players - including the Potters' record signing Peter Crouch, winger Matthew Etherington and first-choice goalkeeper Asmir Begovic - did not make the trip to Ukraine and Pulis named a starting line-up which featured eight changes from Saturday's Barclays Premier League win over Liverpool.
His decision to send the side out in a defensive formation seemed to work well as Stoke soaked up Dynamo's pressure, although the manager suggested it had been chiefly dictated by the squad he had been left to pick from.
"We played the way we did because of the personnel we had today (Thursday)," Pulis said.
"Usually we play 4-4-2 but we didn't have the players to do that, so we decided to change it and worked for a couple of days on the system.
"It suited the players I had better than 4-4-2 - that is the only reason we did that."
Although generally content with his side's performance, Dynamo coach Yuri Semin felt their play could have been more incisive.
"I was satisfied with how my team played, particularly in the first half," Semin said.
"But I think we needed to be more aggressive in the box.
"Stoke really only made one chance on goal and scored it, but this is football."