Brown Ideye and Saido Berahino scored second-half goals to secure a vital victory that lifted West Brom to 14th in the Premier League, four points clear of the relegation zone.
The hosts found another gear after a poor first half to record their second league win under Pulis, but the former Crystal Palace and Stoke City manager insists there is still plenty of room for improvement.
"It was a good performance so we are pleased, but we know it's small steps towards where we want to go and we need to keep our feet on the ground," Pulis told BBC Radio 5 live.
"We played well as a team, both in possession, and out of possession and we looked like a team. It was the best performance since I have been here, against a good side."
Ideye was the standout performer on the night, scoring the opener and laying on the second for his strike partner.
The club's record signing has now scored twice in his past two games, having netted just once in the first half of the season.
It had appeared that the Nigerian striker would leave the club in January, but he remained as other deals fell through and has impressed Pulis with his attitude.
"He's a lovely lad," added Pulis.
"He works hard, his training is good, he is a good professional. He's had a bad time here, before I came in he played quite a few games, not scored the goals the club expected him to score and the pressure just built up.
"Fortunately, we have played him in a few a games and he has done really well and his attitude has been first class.
"We are really pleased that he has stayed and delighted that he has got us a couple of goals.
"In today's world there is no patience, people expect, expect and expect."
