Parker's Cottagers blasted three goals inside the opening half hour, with the hosts down to ten-men thanks to John Swift's red-card.
The win pushes Fulham up to fourth on the Championship table after 10 games.
Speaking after the match, Parker said: "I was delighted with the performance.
"I've been delighted with the performances over the past four or five weeks but the results have been missing a little bit.
"That's what most people usually look at and I understand that. But tonight, I thought that we were first class from start to finish.
"In the first 30 minutes, we were devastating - even though they had a man sent off.
"But, prior to that, I felt that we had really stamped our authority on the game and showed our quality.
"We're going to be a team very hard to deal with in the first 20 or 30 minutes. Even when Reading had 11 men, it was still difficult for them.
"We moved the ball very quickly and with an intensity. And we were really clinical in the final third.
"Over the past few weeks, we've worked a lot on getting that cutting edge about us."