Dutch Cup final: De Jong double gives Ajax edge
This year's final is being staged over two matches, without away fans. Threats from rival groups would have resulted in an expensive and massive security operation.
De Jong opened the scoring after six minutes and made it 2-0 with a fine volley.
"We had a great start with two early goals but after that we lacked a bit of passion up front and were too sloppy in the final pass," Ajax manager Martin Jol told reporters.
Ajax's next big test is next Sunday in the last league match of the season. They trail leaders Twente Enschede by one point.
Feyenoord lacked offensive power and came no nearer than long shots by Denny Landzaat and Luigi Bruins.
But coach Mario Been said: "We still believe we can overcome this defeat at home with a capacity crowd of our fans and that will be different."
The second leg is on May 6.