It was the home side who made the better start to the first-leg affair in Croatia, with Marin Tomasov in particular looking lively as he rattled the post and fired one narrowly over early on.
Aberdeen thought they had a crucial second before the break when Peter Pawlett found a way through, only for the officials to rule it out for offside.
There was to be no denying the midfielder seven minutes after the interval, however, as he converted Logan's back-post cross to put the Scottish club in control.
More joy was soon to come for Derek McInnes's charges, with Kenny McLean adding a third from another deep cross into the box against a Rijeka side boasting a strong home European record prior to this evening.
Ward had to be alert to keep his side's three-goal advantage intact, but having done so the Dons were able to see out the remainder to leave themselves in control heading into next week's reverse tie.