Substitute Walker netted a sublime winner on 81 minutes, while Gordon made an outstanding save from Pars winger Ryan Dow in the first half.
It is the not the first time Gordon has wowed his goalkeeper with some of his performances this season, but he admitted that he has come to “expect” it from his No.1.
"I thought both goalkeepers produced some really good saves,” said Neilson. “It was a really tight game, as it always is when you are playing a team up at the top of the league beside you.
“Yes, Craig had a couple of good saves but we have come to expect that of him.
“He had nothing to do at Raith on Tuesday and today he has really helped us get the three points.
“I see it every day in training, to be honest with you. The more games he gets the sharper he seems to be getting.
“I’m delighted for him. He said when he came here it was to get first team football and try and get in the Scotland squad.
“And watching that today there’s no doubt he should be in there."
The match was evenly poised and appeared to be heading for a 0-0 draw until a moment of magic from Walker, who spun Dunfermline captain Euan Murray and placed a shot beyond Owain Fon Williams to secure the victory.
“Jamie brings that quality,” said Neilson. “He didn’t start today, he had a wee problem with his groin for a couple of days after the Raith game.
“But we knew we would get 20-25 minutes out of him, and bringing him on when the game was more open suited him. His quality showed.”
Neilson also accepted that the overall performance failed to live up to previous heights.
“I think we have played better, definitely,” he added. “Tuesday night was a great performance, today was more of a grind.
“But sometimes you need to do that to win a league.”