Ajax safely negotiated their tricky-looking tie against Eredivisie rivals FC Utrecht to seal their place in the third round of the KNVB Beker.
Ajax, who have won the competition a record 18 times with their most recent success coming in 2010, are just a point above fifth-placed Utrecht in the Eredivisie but they took early control and never looked back as they sealed a 3-0 win.
Tobias Sana put the visitors ahead in the 11th minute and then Ryan Babel made it 2-0 four minutes later before a Christian Eriksen strike just after half-time completed the scoring.
FC Twente were also victorious as they continued their impressive start to the season, although they found it much harder than Ajax before seeing off the challenge of minnows RVVH.
Twente, cup winners in 2011, are four points clear at the top of the Eredivisie after winning their opening six matches but they needed a 90th-minute goal from Luc Castaignos to defeat fourth-tier RVVH.
Feyenoord, who are second behind Ajax in terms of wins in this competition with 11, beat top-flight rivals NEC Nijmegen 3-2 in their second-round match after extra-time, Lex Immers netting the winner in the 120th minute.
Iceland international Alfreo Finnbogason struck a hat-trick as 2009 cup winners Heerenveen defeated Kozakken Boys 4-0 while Heracles Almelo, who were beaten by PSV Eindhoven in last season's final, won by the same scoreline at Lienden
Vitesse Arnhem, second behind Twente in the Eredivisie, netted three second-half goals to beat Gemert 3-0 and join the procession of top sides going through.
However, there were a couple of upsets as well with Willem II and Volendam both tumbling out.
Top-flight strugglers Willem II were beaten 2-0 at home by second division FC Dordrecht, while Volendam, who are fourth in the second tier, were knocked out 1-0 by third division amateur side Rijnsburgse Boys.
Other winners tonight included NAC Breda, FC Groningen, ADO Den Haag, Cambuur, Telstar, HBS, XerxesDZB and SWZ Boso Sneek.