Jon Walters' early goal gave Stoke the perfect start at the Stadium of Light and their task appeared to be boosted when Sunderland midfielder Craig Gardner was sent off for a challenge on Charlie Adam on 34 minutes.
However, Sunderland improved after the break and equalised through John O'Shea on 63 minutes before seeing Danny Rose strike the outside of the post late on.
Pulis told Sky Sports: "It was a hard-earned point and we knew it was going to be.
"When the sending off happened, we had a couple of players booked and coming in at half-time, they were a bit nervous as anything could have seen them leave the pitch.
"I've got to give Sunderland a lot of credit, they showed a lot of spirit and togetherness, so I'm pleased we got the point.
"It takes us to 41 points. There are lots of clubs down there fighting this time round and I'm amazed it isn't sorted out yet. It seems to have happened at all levels, not just the Premier League."
The result moved Stoke six points ahead of the relegation zone and, with games against Tottenham and Southampton to come, Pulis is hoping for a positive end to the season.
He added: "I'm absolutely delighted to have come away with 41 points. We're 11th in the Premier League.
"People get carried away with Stoke City and everything else, but we're 11th with two games to go.
"If we pick up a couple of wins, it would equal our record number of points in the Premier League and I hope we can finish in the top half, which would be absolutely brilliant for us."