The visitors dominated the game from the off as they controlled possession, but the Eagles were resilient at the back for the opening 20 minutes.
However, the pressure finally told in the 28th minute when Feyenoord took the lead as Elvis Manu raided down the flank and cut the ball back to Colin Kazim-Richards. The forward's attempted pass to Jens Toornstra was then turned into his own net by Giliano Wijnaldum.
The visitors doubled their lead when Manu raced down the left again and lifted a cross to the back post, which was turned into the net by an unmarked Toornstra.
After the break, Feyenoord scored their third goal of the evening when Kazim-Richards picked up the ball 30 yards from goal and took a touch to get it out of his feet before launching an effort into the top corner.
Fred Rutten's side sealed their victory in the 89th minute when once again Manu turned provider as he raced into the box before cutting the ball back to Mitchell te Vrede, who was left with a simple tap-in.