Well had won the first leg 1-0 and they completed the job on Thursday night, with Jamie Murphy grabbing the only goal three minutes before the break when he latched on to a long Stephen Craigan free-kick to slide the ball past home keeper Ingvar Thor Kale from around 12 yards.
That strike dampened the enthusiasm of the Icelanders who had missed several good chances in the first half and in the end, despite a few more scares in the second half, it was a comfortable enough win for the Lanarkshire men.
Motherwell will face Norwegian side Aalesunds in the next round with an away game on July 29 and the return at Fir Park seven days later.
Breidablik stuck with the same X1 which lost narrowly in Lanarkshire while Well boss Craig Brown made one change, defender Steven Saunders coming in for Chris Humphrey who started on the bench with Tom Hateley moving in to midfield.
The Fir Park men started positively, pushing for the goal which would leave their opponents needing three to go through.
However, it was the home side who almost scored five minutes in to the game but captain Kari Arsaelsson headed just wide of the target.
As the game unfolded both teams appeared well aware of the significance of the first goal and it looked likely it would fall to the Icelandic side.
In the 20th minute Breidablik forward Gudmundur Petursson had a drive which flew over the crossbar after Craigan headed a free-kick from Kristinn Jonsson 25 yards clear.
Moments later, though, Ross Forbes, who scored the goal at Fir Park in the first leg, may have been expected to work the home keeper after good build-up work by Keith Lasley and John Sutton but he too failed to hit the target.
The Icelandic league leaders, playing in Europe at home for the first time, edged the first half and in the 36th minute Petursson again missed a good chance with the Motherwell defence defending desperately, Saunders throwing himself to block the effort.
In the 42nd minute the home side paid for their profligacy in front of goal when the pacey Murphy grabbed the opener, his record-equalling fifth European goal for the Fir Park side.
It looked a long way back for the home side but minutes in to the second half, amid some more hesitancy in the Well defence, Gudmundur Krisjansson eased past Saunders on the left-hand side of the box but could only hit the side netting with his drive.
In the 54th minute, after Elfar Freyr Helgason had fouled Murphy 25 yards from goal, Forbes crashed a free-kick against the post and back in to the keeper's arms.
Much of the zest had disappeared from Breidablik's semi-professionals and Motherwell appeared content to see out the second half.
In the 73rd minute though, moments after Arsaelsson's header was cleared off the line by Mark Reynolds, Alfred Finnbogason dipped a shot from 20 yards over the bar.
There were more near misses at both ends in the final stages but Motherwell were able to cruise to the final whistle with the prospect of another long journey to Norway next week.