Though much changed since their 3-0 victory against Gibraltar a month ago, they appeared the more likely to score in the early exchanges, though Petar Sucic made a mess of the first chance after a superb cross from Ivan Perisic.
Then, on 15’, Josko Gvardiol’s loss of control by the halfway line allowed the Faroes’ Geza Turi to take possession. After a run to the edge of the area, he unleashed a shot that deflected past Dominik Livakovic and silenced the home support.
Jakup Andreasen then looped a header against the post, as Croatia wobbled again, but Gvardiol redeemed himself in the 22nd minute with a superb left-foot equaliser that was drilled past Mattias Lamhauge.
Hanus Sorensen had a run on the home defence too, with Livakovic stretching out a left foot to save a certain second goal from the visitors.
As the half wore on, though, the class of Luka Modric began to tell, and his first-time shot from 20 yards had to be palmed away by Lamhauge to keep the scores level.
To the Faroe Islanders’ credit, they made their hosts work hard for the upper hand, with Gunnar Vatnhamar cutting a particularly impressive figure in a first half that ended all square.
Modric was again the beating heart for Croatia as they put the visitors under immediate pressure after the break.
Andrej Kramaric somehow missed a free header when unmarked in the box, but shortly after, Petar Musa’s superb control and shot inside the area handed the hosts a deserved lead.
With the Faroes resorting to putting 10 men behind the ball, it only invited more Croatian attacks, and Perisic was next to go close to extending the lead.
With 20 minutes to play, Perisic then put on the afterburners to outpace Viljormur Davidsen and provide a sumptuous cross for Nikola Vlasic to volley home at the far post.
The remainder of the game was an exercise in keep-ball from the hosts, though Petur Knudsen and Andreasen did at least work Livakovic late on.
Despite a brave attempt, the Faroes’ fifth defeat in six away games has ended their faint hopes of qualification to next summer’s tournament.
Flashscore Man of the Match: Ivan Perisic (Croatia)