Stoke had only won once this season ahead of the clash with Mark Hughes' side, but a Charlie Adam strike settled a closely-fought contest.
Pulis was delighted with the points as his side maintained their unbeaten record at the Britannia Stadium, insisting it was vital to grind out wins at the same time as trying to 'evolve' as a team.
"We've played really well this season and not got results, and today was much more of an even game," he told Sky Sports.
"But we've got the result and the result was the most important thing today, to give us a little bit of confidence and get that monkey off our back.
"But our home form has been terrific again, if you look at the results we've had.
"And it's another clean sheet for us at home, which is brilliant because this place has to be a fortress for us.
"We are trying to evolve the team a bit in some ways, but that takes time and we have to make sure we pick points up along the way as well."