The Magpies were 2-0 ahead before the half-hour thanks to a John Heitinga own goal before a stunning Ryan Taylor strike.
But Everton pulled a goal back in first-half injury time through Jack Rodwell and the hosts had to hang on after the break after they lost French duo Yohan Cabaye and Sylvain Marveaux to injury.
"It was one of those games today where we got disrupted," Pardew told Sky Sports 1.
"We lost two key players, but the guys who came on did well.
"It shows another side of us - that we have strength in depth.
"They had their big guns come off bench and come at us but we defended solidly. It was one of our best defensive performances.
"We had that disruption and we lost our rhythm but we kept ball and were clever."
Newcastle are now unbeaten after 11 games to start the season and moved second in the Barclays Premier League table, for a couple of hours at least, with Manchester United able to jump back ahead of them when they host Sunderland this afternoon.
"It's great (to be second)," Pardew added.
"But I think Fergie will have some say later on.
"We had some great performances today."
Pardew also praised the impact of the Newcastle fans as his side sought to hold onto their lead in the second half.
"Their support got us across the line," he said.
"We wouldn't have got that result at Goodison. 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."
Everton boss David Moyes was left to rue missed opportunities, and in particular the decision by referee Andre Marriner to deny his side a penalty, as the Toffees stretched their recent run to six defeats in seven games in all competitions.
He said: "If you look at chances, we probably had more chances than Newcastle in the first half and we were on the verge of going in 2-0 down, so the goal before half-time gave us a real lifeline.
"But we couldn't quite get the opening or opportunity. We didn't get as many chances in the second half, albeit I have seen it and it is a stonewall penalty when it hits his hand.
"The ball was going in as well, so it had beaten the goalkeeper, the goalkeeper wasn't getting it."