The Dutch outfit carried a 2-0 advantage to Slovakia from the first leg, and were never in any real danger of slipping up.
Hans van der Haar netted a goal in each half as Foeke Booy's side proved too strong for Zilina.
Michael Lamey and Stefaan Tanghe netted late goals to put some gloss on the scoreline and propel Utrecht into the second round.
NEC Nijmegen bowed out of the competition, 4-2 on aggregate, after losing 2-1 at home to Wisla Krakow on Wednesday.
Wisla came to Holland with a narrow cushion, but that was wiped out when Mike Zonneveld netted on 33 minutes.
However, the Poles recovered and two goals from Tomasz Frankowski took Wisla to victory.
NEC lost all control, and could face Uefa censure, as Youssouf Hersi, Patrick Ax and Zonneveld were all sent off.
