The visitors, who captured the imagination of millions of spectators by reaching the Euro 2016 quarter-finals, began where they had left off in France by taking a fifth minute lead through Alfred Finnbogason.
Iceland should have gone further ahead when Jon Dadi Bodvarsson's shot a close-range effort straight at goalkeeper Andriy Pyatov, then sent the rebound flying over an empty goal in the European Group I match.
Ukraine, playing their first match under new coach Andriy Shevchenko after he replaced Mykhailo Fomenko following Euro 2016, levelled four minutes before halftime with a goal by Andriy Yarmolenko.
They took control after halftime and Yevhen Konoplyanka was close with a long-range effort which Hannes Halldorsson managed to save.
The home side had an even better chance five minutes from time when they were awarded a penalty, however Konoplyanka's effort shaved the outside of Halldorsson's right post.
(Writing by Brian Homewood in Berne; Editing by Rex Gowar)
