Jason Puncheon's 16th-minute strike was enough to secure a second successive victory and moves Pulis' side up to 14th in the Premier League table.
Palace had to withstand plenty of pressure from Hull in the second half, but their defence remained defiant and Julian Speroni was rarely tested, leaving Pulis delighted at a crucial three points.
The former Stoke City boss also reserved special praise for Puncheon, and hopes the winger can keep his form going after match-winning strikes in consecutive home games.
"It's a massive three points for us," he said after the victory on Tuesday. "To get three points and keep a clean sheet again is smashing.
"If you keep working with him, Punch is a Premier League player and can win games.
"When you get a knock, the most important thing is that you get up as quick as you can. Punch has done that."
The win puts a five point gap between Palace and the bottom three, but Pulis has no intention of letting his side lose focus in their fight against relegation.
"We still need 17 points from 15 games which is a massive task for us," he added. "We won't get carried away.
"We are pleased, but we can't take our eye off the ball or take our foot off the pedal.
"I won't take any satisfaction until the end of the season when we've got those 40 points."
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