Ajax dominated the match against a Roda side who sold Syria striker Sanharib Malki, their top scorer last season with 17 league goals, to Turkey's Kasimpasa in the transfer window.
Ajax found the net twice in the first half in balmy temperatures but could have scored more against Roda, who survived the relegation play-offs last term and were plagued by injuries and suspensions for their season opener.
It took Ajax only 10 minutes to grab the first goal of the new campaign through full-back Van Rhijn who pounced on a rebound after Roda goalkeeper Filip Kurto dropped a free-kick by Denmark midfielder Christian Eriksen who then set up De Jong's goal.
Roda had chances in the second half but Hungary striker Kristian Nemeth hit the post after a defensive mistake and midfielder Wiljan Pluim blasted over from the spot after Daley Blind gave away a penalty with 20 minutes to go.
It was the fifth penalty miss in a row against Ajax and nine minutes later Fisher made Roda pay with Ajax's third goal.
De Jong, playing the 150th Eredivisie game of his career, conceded that Ajax never played at 100 per cent.
"I heard that it looked that way from the stands. And, to be fair, it could well be the case especially halfway through the second half when we lost our concentration," he said.
"But after the penalty miss we found our rhythm again. And when we scored our third, it was all over."
On Saturday, last season's Dutch championship runners-up PSV Eindhoven open their campaign at ADO Den Haag while third-placed Feyenoord visit PEC Zwolle on Sunday.