The win meant Iceland, who delighted the sports world by reaching the quarter-finals of Euro 2016 last year, went level on 16 points with Croatia at the top of Group I. Croatia, beaten 1-0 by Turkey, lead on goal difference.
Iceland went ahead two minutes after halftime, although Ukraine were deeply unhappy about the goal.
Emil Hallfredsson whipped in a low cross from the left, Ukraine goalkeeper Andriy Pyatov got to it but dropped it as an Iceland player collided with him, and the ball ran to Sigurdsson to score into an empty net.
There were no questions about the second goal, however. When the ball was fed in from the right, Hallfredsson dummied and Jon Bodvarsson laid the ball off to Sigurdsson, who fired past Pyatov from the edge of the area.
Iceland's last two games are a tough trip to Turkey and then a home match against Kosovo, who have taken one point from eight games.
The nine group winners qualify directly for Russia and the best eight runners-up take part in a playoff round for a further four places.
(Writing by Brian Homewood; Editing by Hugh Lawson)
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