The visitors should have taken the lead on 50 minutes when Steven Davis sent McGinn clear, but the Celtic winger could only find the side-netting from a tight angle after rounding Mikkelesen.
Healy replaced Warren Feeney and the substitute made an immediate impact with a low shot which had Mikkelsen at full-stretch.
Mikkelsen again thwarted Lafferty after 58 minutes when he clawed out the striker's header which was arrowing into the top corner.
The Faroes scored with their first meaning attack of the second half - Stephen Craigan's poor touch gifted possession to the Faroes and Udsen played in Holst, who wriggled free 10 yards out before shooting across Taylor and into the bottom corner.
Northern Ireland wasted two opportunities to draw level within minutes of the goal with Chris Baird and Evans heading wide from close range.
Evans sent a looping header onto the roof of the net before Northern Ireland finally converted one of their chances.
Lafferty jinked by three players on the edge of the box and played a one-two with Brunt before firing a crisp low shot into the bottom corner from 20 yards.
Lafferty went close to netting again a minute later but he guided the ball straight at Mikkelsen from Brunt's cross.
Northern Ireland piled on the pressure in the closing stages but the Faroes defended bravely to secure a rare point.
The result sees Northern Ireland slip a place to fourth after Slovenia earned a 1-0 win in Estonia.
The match between Group C leaders Italy and Serbia in Genoa was abandoned after seven minutes due to crowd trouble.
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