
Rosenborg, who last season missed out on the Champions League for the first time in 12 years, had an ideal start at Kazakhstan's FK Astana when Burkina Faso striker Yssouf Kone headed in after just six minutes.
The home side drew level through captain Aleksandr Kuchma, who scored with a direct freekick in the 27th minute.
Just on the hour Kone was fouled in the area and Steffen Iversen made no mistake from the spot. A few minutes later Kone gave his side a convincing victory with a well-struck shot from an acute angle.
In Latvia FK Ventspils were no match for Giovanni Trapattoni's Red Bull Salzburg. Austrian international Rene Aufhauser scored twice within the space of a few minutes midway through the first half to give Salzburg a 2-0 half-time lead.
The midfielder added a penalty late in the second half for his hat-trick.
The return leg matches will be played next week, with the winners of the ties advancing to the final qualifying round.
DPA