Daniel Sturridge then sealed a 2-0 victory with a goal two minutes after half-time.
Wilkins said: "From our perspective Nicolas is playing some outstanding football. He is a joy to have around the place.
"He enjoys his training, he is working extremely hard and he is getting the rewards from that."
Anelka's goal came when he brushed past Youl Mawene and fired in a shot that had too much power for impressive goalkeeper Andy Lonergan.
Preston should have equalised but Darren Carter somehow steered the rebound wide after Hilario had palmed away a header from Chris Brown.
It proved to be the turning point as Sturridge added a second two minutes in the second half after John Terry's header rebounded to him.
It was Sturridge's third goal since he arrived from Manchester City in the summer and Wilkins said: "We are pleased with Danny.
"He has a lot of talent and is working extremely hard. For young players at Chelsea it is really difficult to get past the likes of Nicolas and Didier (Drogba). But he is looking a good player."
England midfielder Frank Lampard came off with tightness in his calf as a precaution but Wilkins had little to complain about.
He said: "We put out a strong team to show what we think of the FA Cup. We are the holders and want to retain it.
"It was a professional performance by our guys and we are delighted to be in the hat. We scored at good times in the game. We were able to get a foothold in the match.
"It is not easy to come to a Championship side. The ground was packed and Preston put us under pressure at times. We had to defend our box at times but we did that well."
It was Darren Ferguson's first home match as Preston manager and he praised his players for the shift they put in.
However he was left to reflect on Carter's clanger that changed the face of the tie.
Ferguson said: "There are always key moments in games. A minute before half-time we missed a great chance. But I told Darren to keep getting in there. I don't want people hiding.
"Then we lost a disappointing goal to a set-piece and that killed the game.
"The fans were brilliant and gave me a great reception. They want to see effort and commitment and we gave them that.
"Chelsea are a fantastic team and you have to give them credit for the way they play."