Goals from Niall McGinn and Jonny Hayes ended any Aberdeen anxieties as they made it through to the Europa League third qualifying round.
After a sterile first half Rijeka threatened a miracle recovery from their 3-0 aggregate deficit when Marin Tomasov scored with a sublime strike.
Substitute Zoran Krvzic then netted with the aid of a deflection.
But McGinn raced clear to fire in and Hayes drove home as the Dons progressed to face Kairat Almaty of Kazakhstan.
Manager Derek McInnes made it clear Aberdeen would need to do a professional job to see out the tie despite the impressive 3-0 first-leg win in Croatia.
Kenny McLean was preferred to Peter Pawlett in the starting line-up as an indication that the manager was as keen to keep a clean sheet in the return as he was to add to their aggregate lead.
David Goodwillie was once again the lone striker with everyone in a red jersey apart from him quick to get back into a good defensive shape whenever Rijeka were in possession.
As a result, the visitors, who had made the group stages for the last two years, often ran into dead ends when they tried to find the space in the first half.
Andrew Considine and Graeme Shinnie in particular impressed when called on to make important interventions while Ryan Jack controlled the midfield and the pace of Hayes on the counter attack always carried a threat.
Hayes carved out Aberdeen's first real chance with a great run and cross that goalkeeper Simon Sluga could not cope with and McLean was inches away from what would have been a back-post tap-in.
Croatia Under-21 cap Sluga was brought in after Ivan Vargic's poor performance in the first leg and justified his selection on the stroke of half-time when McGinn threatened a breakthrough.
The Northern Ireland international cut into a central position before hitting a shot from the edge of the box that Sluga brilliantly parried just when it seemed destined to nestle in the corner of the net.
But, in a rather surprising start to the second period, the visitors finally found a cutting edge with Tomasov producing a bit of magic.
The former 1860 Munich winger eased past two challenges at the edge of the box before curling a shot beyond Danny Ward into the bottom right hand corner of his net.
Even then the Dons looked comfortable but a speculative shot from Kvrzic took a big deflection off a defender to loop into the net and put the tie back in the balance.
Only for seconds, though, as McGinn, who scored the vital away goal in the previous round, latched on to Goodwillie's pass in to score.
And then Hayes, who previously missed a sitter, made amends by finishing from another fine pass by Goodwillie.
The 5-2 aggregate win was built on an impressive win in Croatia achieved in the most difficult of circumstances but, logistically, things will be even tougher for McInnes's men in the next round.
They will face a 9,000-mile, 15-hour round trip across five time zones to face Kairat after the Kazakh side defeated St Johnstone's Europa League conquerors Alashkert of Armenia 4-2 on aggregate.
- 2LoganBooked at 90mins
- 10McGinnSubstituted forFloodat 83'minutes
- 3ShinnieBooked at 71mins
- 7McLeanSubstituted forPawlettat 73'minutes
- 17GoodwillieSubstituted forRooneyat 75'minutes
- 18BradaricSubstituted forBalajat 74'minutes
- 23RoshiSubstituted forKvrzicat 52'minutesBooked at 67mins
- 88Lima Magalhães
- Marco Guida
- Shots on Target