Ajax, who won the first leg of the final 2-0 thanks to goals from De Jong, sealed their 18th Dutch Cup 6-1 on aggregate.
Suarez opened the scoring in the fourth minute with a long drive which was misjudged by Feyenoord goalkeeper Erwin Mulder.
Martin Jol's men, who finished a point short of champions Twente Enschede in the title race, were never seriously troubled by Feyenoord and settled the match after 64 minutes with De Jong's first goal.
Eight minutes later Jon Dahl Tomasson pulled one back on the rebound after a free-kick from Jonathan de Guzman hit the post.
But De Jong quickly restored the two-goal lead before Suarez added a fourth.
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