Ajax keep pace in Eredivisie
El Hamdaoui opened the scoring two minutes before the interval for Frank de Boer's side and De Jong sealed the points 11 minutes from time. The result kept third-placed Ajax in the title hunt, three points behind leaders PSV Eindhoven, while De Graafschap remained 12th.
It could all have been different had De Graafschap taken advantage of the game's first chance after 13 minutes at the Amsterdam ArenA, but Tyrone Loran's header from Jordy Buijs' corner flew narrowly over the bar.
Toby Alderweireld's free-kick just after the half-hour mark, which was too high to test Boy Waterman, looked like being the best Ajax could muster in the first half before El Hamdaoui popped up with the opener. Surrounded by De Graafschap defenders, Miralem Sulejmani fed El Hamdaoui and the Morocco forward made no mistake from close range.
Sulejmani went close to doubling his side's lead 13 minutes into the second half with a long-range shot but it fizzed just wide.
Steve de Ridder almost made Ajax pay four minutes later with a thunderous blast from just outside the box, but the crossbar came to the hosts' rescue and the ball was scrambled to safety.
The Amsterdammers wrapped up the points in the 79th minute, Christian Eriksen's left-footed cross finding De Jong, who fired his shot under the body of Waterman. Ajax could have made it 3-0 three minutes later when Vurnon Anita tried his luck from 18 yards, but his effort crashed against the bar.