The visitors were denied an early opening goal when keeper Luciano saved a shot from Derk Boerrigter then De Jong made no mistake after 25 minutes with a shot from 20 metres that went in off the post.
Four minutes into the second half Eriksen made it 2-0 with a superb running volley that went over Luciano and Boerrigter set up Fischer to settle the match in the 60th minute.
"We played very effectively today although we didn't create many chances but we controlled the match," said Ajax skipper De Jong.
"Our early second goal was decisive as Groningen changed their tactical plan after the break by playing one-on-one in their defence to try to get back in the match."
Ronald Koeman's Feyenoord beat Marco van Basten's Heerenveen 7-6 on penalties on Wednesday to reach the quarter-finals, joined by Vitesse Arnhem who hammered amateurs ADO'20 Heemskerk 10-1.
Holders PSV Eindhoven also reached the last eight with a comfortable 4-0 win at Rijnsburgse Boys on Tuesday.