Derek McInnes’ side were the underdogs going into the first-leg tie against the side who finished second in the Croatian league last season.
However, the Dons overcame the heat in the Balkans thanks to goals from Andrew Considine, Peter Pawlett and substitute Kenny McLean.
Aberdeen were expected to be up against it in the Stadion Kantrida and it was the home side who started the brighter.
Marin Tomasov was Rijeka’s danger man early on, latching on to a ball over the top of the Dons’ defence just four minutes in and firing inches wide.
A couple of minutes later, his close-range effort rattled the post before he completed a hat-trick of misses after 11 minutes when he fired a free-kick over the bar.
The visitors started to come into the game shortly after and looked dangerous on the counter attack but it was Dons keeper Danny Ward who was called into action to brilliantly deny Lima Magalhaes’ header.
Despite the home side’s excellent start, it was Aberdeen who took the lead after 37 minutes as Considine popped up at the back post to head into the net after meeting a Niall McGinn corner.
The Dons thought they had doubled their lead five minutes later when Jonny Hayes crossed for Pawlett to score but his header was ruled out correctly for offside.
The midfielder was not to be denied for long, however, and there was nothing wrong with his diving header just six minutes into the second half.
Shay Logan’s deep cross was a good one and Pawlett somehow managed to get enough power on his header from 16 yards to beat the diving Ivan Vargic
Aberdeen were comfortable after doubling their lead and Hayes went close to adding to the scoreline but his header was well saved by Vargic.
Substitute McLean sent the small band of Dons fans into dreamland shortly afterwards when David Goodwillie set up the defender to volley his first goal for the club.
Ward was called into action again in the dying minutes when he made a great block in the six-yard box to keep out Roman Bezjak but Aberdeen will take a sizeable advantage back to Pittodrie for the return leg next week.