Jack Rodwell responded for the visitors but Newcastle managed to hold on to claim three points in front of their home faithful.
"Their support got us across the line," said Pardew. "We wouldn't have got that result at Goodison [Park]. They would have beaten us or certainly got a draw.
"They help us and pull us through. They are absolutely brilliant, our fans, and we certainly don't take them for granted."
Newcastle remain unbeaten in the Premier League after eleven games of the season.