The hosts took the lead early on as Gary Hooper saw his shot deflect over David Stockdale, but Fulham reacted well to going behind.
Pajtim Kasami drew the visitors level just after the half-hour mark as his free-kick went straight through the Norwich wall and into the bottom-right corner of the goal, before Parker secured all three points with a wonderful strike in the final five minutes.
The win was only their second in 10 Premier League fixtures and Meulensteen was particularly glowing about the impact on the team of England international Parker.
He said: "It could be a very significant goal, but we can only tell when months and months go by. I'm delighted with the three points, I'm delighted with Scott scoring the winner.
"His leadership, character and performances on the pitch have typified us over the last few weeks and today was no different.
"He is very important as captain and leads by example in every game we play."
Meulensteen also spoke in glowing terms of Alan Curbishley's appointment as technical director.
He added: "I've not spoken to Alan, but I'm absolutely delighted about the appointment and that he has joined us.
"It was something the club were looking to do even before I joined the club so there is no surprise there. It was just a question of finding the right combination.
"He will provide me with fantastic support due to the experience he brings to the table. I'm happy he was here. He saw us, our team spirit.
"So from now on I hope he can add to it and enhance our chances of staying in the Premier League."
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