The result left Croatia top of the section on seven points from three games.
Looking a little flat after demolishing the Kosovans, Croatia were in control apart from a spell of second-half sporadic pressure from the home side.
The home side failed to create a clear-cut chance on a difficult pitch while, at the other end, Ivan Perisic hit the inside of the post in the 75th minute after a solo run.
Finland keeper Lukas Hradecky twice denied substitute Duje Cop in the closing stages as the home team ran out of steam and Croatia finished on a high note.
(Writing by Zoran Milosavljevic in Belgrade; Editing by Neil Robinson)
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