Torshavn enjoyed a touch more of the ball in the first period and were able to carve out greater chances than the visitors.
But Derry did work their way into the match as time went on.
In fact, the League of Ireland Premier Division outfit effectively dominated much of the second period.
Ultimately, though, Torshavn defended well and were able to keep out a late push by Derry.
Both sides go into the second leg of their Europa Conference qualifier next week with it all left to play for.
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