Rooney took his tally over the two ties to five as the Dons won 3-0 in Latvia for an 8-0 aggregate victory.
Aberdeen went into the game knowing the tie was safe but there must have been some concerns over the approach of the Latvian side, who had two men sent off and a further five booked at Pittodrie.
But there were no bookings at all in the Latvian capital as the Dons produced another convincing display to set up a second-round clash with Dutch side Groningen, although they lost Jonny Hayes to injury in the second half.
Aberdeen boss Derek McInnes brought in Ashton Taylor for his debut at left-back, allowing Hayes to move further up the park in place of the injured Peter Pawlett, who was kicked off the ball in the first leg. Andy Considine also came in with Russell Anderson rested.
The hosts made a decent start but Emils Knapsis and Mantas Savenas fired over when presented with early chances and the Dons quickly took control.
Niall McGinn came close after a good knockdown from Rooney, who soon opened the scoring in the 22nd minute after a spell of pressure.
Rooney's deft touch lifted the ball over the home goalkeeper after Hayes had crossed to the near post.
Jamie Langfield made a good stop from Knapsis after a ball over the top caught the Dons out before Shay Logan fired just wide at the other end.
Rooney netted again in the 40th minute after home goalkeeper Janis Krumins, who did not play at Pittodrie, missed Logan's cross and allowed the former Inverness striker an easy tap-in.
The forward completed his 23-minute hat-trick just before the break after great play from Hayes, who burst into the box and played the ball to the back post for Rooney to sweep home.
Hayes went off injured just after the hour mark with Cammy Smith coming on and it was a quiet second half as Aberdeen played out the game.
Nicky Low and 16-year-old midfielder Scott Wright came on as the Dons comfortably saw off Daugava's attempts to force a consolation goal.