The former Oldham striker took his Europa League tally to five goals in two games as the Scottish Premiership side wrapped up a facile 8-0 aggregate success.
The Dons had made short work of their Latvian opponents in the first leg last week and any thoughts of a unlikely turnaround were quickly dashed as Rooney (21) latched onto Jonny Hayes' cross to open the scoring.
In bright Baltic sunshine the Scottish side were being cheered on by a healthy band of travelling supporters, whose mood was further enhanced as Rooney completed his hat-trick (40 & 44) with two more predatory finishes.
FC Groningen visit Pittodrie in the second qualifying round next week; the Dutch side ended their season with a 10 game unbeaten run, defeating AZ Alkmaar 3-0 on aggregate in the play-offs to qualify for European football for the first time in seven years.
Aberdeen boss Derek McInnes said: "In general the approach was spot-on, as it had to be to give them no encouragement. We asked the boys to be professional. It was a mature and competent performance, just what was required.
"The pace of the game dropped in the second half, understandably, we didn't need to chase it and they defended a bit deeper. All in all over the two legs there was a lot to be pleased about but we know there are bigger challenges ahead."