Barcelona left back Jordi Alba put the world and European champions in front in Helsinki after just 19 minutes.
Spain enjoyed plenty of play in attacking areas but the Finns set out to defend in much the way they frustrated La Roja in their previous meeting when they drew 1-1.
However, Vicente del Bosque's charges were getting more reward for their dominance with David Villa failing to convert a good chance before the half-hour mark.
However, the visitors were able to find a winning goal through Manchester City new boy Alvaro Negredo with four minutes remaining.
The result increases Spain's lead at the top of Group I after France could only draw to Georgia.
Meanwhile, Finland face an almost impossible task to reach the playoffs, trailing Les Bleus by five points with two games remaining.