The Dons dominated from the start and Shay Logan headed a 33rd-minute opener from a Jonny Hayes cross after Barry Robson missed an early penalty.
The hosts scored twice within three minutes early in the second half, Niall McGinn netting from close range and then Rooney converting a spot-kick.
Rooney set up compatriot Hayes to net from eight yards in the 73rd minute and the former rounded off the scoring in injury-time when he flicked the ball past the goalkeeper following a Hayes cross.
Daugava, who sit seventh in the 10-team Latvian top flight, never troubled Dons goalkeeper Jamie Langfield and resorted to naked aggression as they struggled to get to grips with the home side, seeing two players sent off and another four players booked.
Aberdeen were starting their season less than eight weeks after defeat to Motherwell consigned them to the first qualifying round but, with their League Cup-winning team intact, they showed little sign of ring rust, although they had enough chances for an even more convincing win.
The Scots suffered a shock European defeat to Skonto Riga 20 years ago and the visitors are 19 games into their season but the Latvian side were nowhere near good enough to defy odds of 25/1 with some bookmakers to win away.