Frank Lampard’s side were already leading 1-0 thanks to Oliver Giroud’s goal before the American made it 2-0.
The move started in the middle of the pitch with Willian playing a give-and-go with Giroud before he found Pulisic down the left.
The American then moved the ball onto his left foot and hammered it past Guaita at his near post to put the Blues in the ascendency.
And Neville, speaking in the immediate to the goal, was left more than impressed with what he had witnessed.
“Really good. He’s impressed me enormously. As he gets one v one, I actually think Ward does all he can – which is shove him on the outside,” he told Sky Sports.
“He’s in trouble, he’s in the box, but you don’t expect that he’s gonna do that. He smashed it. Ordinarily, you’d say ‘Goalkeeper’, but there’s no chance.
“It’s so fast. Devastating from Pulisic. He was wonderful at West Ham in that defeat last week. He’s just set this game alight.
“When you’re a full-back and you’re in a position like that against a really good player, do the very best you can and put him in a position where it’s easier for the goalkeeper, that’s what he did.”
Wilfried Zaha then reduced the arrears before the half-time interval with an absolute rocket from range that flew past Kepa Arrizabalaga but the Blues moved up to third as Tammy Abraham’s second-half goal proved enough despite Christian Benteke pulling one back.