The hosts were dominant in the first period of Sunday's Premier League clash - enjoying 83 per cent possession - and deservedly took the lead via Jonathan de Guzman on 25 minutes.
Eagles boss Pulis changed his formation for the second period, bringing Glenn Murray on immediately after the break and the decision paid dividends, with the striker notching a late penalty - his first Premier League goal after recently returning from a long injury lay-off - to earn a point for the visitors.
Afterwards, the Palace boss insisted the result - which lifted the Eagles three points clear of the drop zone - was for the football club as a whole, rather than individuals.
He told Sky Sports: "It's not about Glenn, it's not about me, it's not about anyone - it's the football club that's really delighted that we've got a point today.
"It's an important point and we've got to pick points up away from home.
"But you've got to give credit to Swansea, I thought they were very good first half and we were, I thought, the dominant side second half."
Pulis confirmed he would be fining Jerome Thomas after the substitute dived in the penalty area late on to try and earn another penalty.
Thomas was booked by referee Mike Dean for his antics and Pulis said diving would cost the player, as well as Marouane Chamakh.
He said: "I've just had a chat with JT about falling over in the box, Cham(akh) did it as well and we'll fine them, they'll pay money.
"I keep on about it to other people about people falling over when they're not touched.
"Thank goodness JT has gone in and seen Mike anyway and apologised himself.
"But it's something we should stamp out of the game, and certainly those two will be fined this week."