Benni McCarthy netted his second goal of the tie against a lacklustre Salzburg side, before David Bentley supplied the icing on the cake with a stunning volley from outside the box.
After grabbing two away goals in the first leg, Rovers would have been looking to keep it tight at the back early on, but they almost gifted the visitors a goal with less than a minute on the clock.
Straight from kick-off, Brad Friedel's poor clearance was played directly into the path of Christian Tiffert, but the German midfielder took too long on the ball and the Rovers defence were able to get back and clear.
McCarthy showed a glimpse of what he was capable of on five minutes, latching on to Bentley's throughball, before turning inside the last defender on to his left foot and forcing a smart save and corner out of Timo Ochs.
Zurab Khizanishvili was forced to hook clear a vicious ball in away from the head of Alexander Zickler on 19 minutes, and when the Georgian defender slipped just five minutes later, Zickler pulled the ball back for Johan Vonlanthen to fire comfortably into the arms of Friedel.
On 26 minutes, Brett Emerton's free-kick found its way through to Morten Gamst Pedersen at the back post and after allowing the ball to bounce, the Norwegian attempted an acrobatic volley, which forced Ochs into a smart reaction save.
Again Rovers threatened on 31 minutes. Following good build-up play, Shabani Nonda pealed away to the far post where he was found by a trademark Tugay pass, but the striker struck a left-foot volley into the side of the net.
The better openings were all falling to the home side and they took a deserved lead just a minute later. Pedersen found McCarthy down the left flank and after arguably an exquisite turn, the South African fired Rovers in front, beating Ochs with a right-foot shot to his near post.
And Hughes' men ought to have made the tie safe on the stroke of half-time. Bentley's brilliant ball in from the right found the unmarked McCarthy in the centre, but somehow the former Porto striker guided his header inches wide of Ochs' left-hand post.
Lucas Neill almost extended Rovers' lead just five minutes after the break following a sumptuous Tugay pass, but the home fans were up celebrating another wonder goal just six minutes later.
Nonda chased down a lost cause before heading down to Bentley and the England Under-21 international chested the ball into the air, before striking a stunning right-foot volley into the top corner of the net from 25 yards plus.
With 20 minutes remaining, Pedersen's fierce free-kick forced Ochs to fumble, but the German keeper then made amends with a brilliant point-blank save from McCarthy, who had just crept offside.
In time added on, substitute Francis Jeffers was twice denied by Ochs after being put clean through, but the 2-0 victory was more than enough to see Rovers progress.