Scotland survived the banana skin of Toftir thanks to first-half goals from Shaun Maloney and Garry O'Connor.
But the Scots rode their luck in the second half as the Faroes dominated and hit the woodwork twice and were unlucky not to get something back.
A second-half booking for captain Barry Ferguson means he will miss the next qualifier against Lithuania.
The game started in predictable fashion with the Faroes sitting deep and trying to frustrate Scotland by closing down space.
Alex McLeish's side won a string of early corners but they all came to nothing with the Faroes defenders dominant in the air.
Maloney did manage to test Jakup Mikkelsen with a 30-yard free-kick which the goalkeeper beat out.
There was a scare for Scotland after 19 minutes when David Weir lost sight of the ball and Craig Gordon had to come out to pluck it off Rogvi Jacobsen's head.
Indeed, Weir had a tug at Jacobsen's shirt in the penalty area but the Greek referee Georgis Kasnaferis did not see it.
O'Connor always looked dangerous and he was desperately unlucky not to open the scoring after 24 minutes.
Kris Boyd knocked the ball into his path and his left-foot shot was touched onto the post by Mikkelsen.
Boyd missed a glorious chance five minutes later when he volleyed over from eight yards after uncertainty in the Faroes defence.
But the goal arrived after 31 minutes after Boyd was fouled by Oli Johannesen on the edge of the area.
Maloney stepped up to curl a wonderful free-kick over the wall and into the net.
O'Connor made it 2-0 ten minutes from the break when he bundled the ball home after Mikkelsen had blocked his initial header.
Jakup Borg wasted a great chance to pull the Faroes back into it early in the second half when he shot over from good position and then Christian Holst stabbed a shot wide from six yards.
Gordon then had to make a couple of saves in quick succession from Suni Olsen in the Faroes' best spell.
The goalkeeper then made a crucial save to deny Borg after he had eluded Weir.
There was a major let-off in the 69th minute when Gordon was caught in two minds at a free-kick and the header from Holst hit the inside of the post.
Substitute Andrew Flotum then struck the crossbar in the final minute as it was clear it was not going to be the Faroes' day.
