Leading 2-0 from the first leg a week ago, David Jeffrey's men completed a comprehensive aggregate win to tee-up a second-round meeting with Greek side Xanthi.
Michael Gault opened the scoring five minutes before the break, with Jamie Mulgrew adding a second shortly after it.
On the hour-mark it was 3-0, as Gault fed Philip Lowry and the midfielder's drive had too much power for keeper Jakup Mikkelsen.
Linfield will head to Greece next week, with the second leg to be played the week after.
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