The start of the match at Merthyr Tydfil was delayed for 50 minutes by a power cut which affected much of the surrounding area.
But once the action got under way, Wales were determined not to put the memory of their 8-1 hammering by the Italians behind them.
Jimmy Shoulder's team battled for everything and could have won had Matthew Williams' free-kick not hit a post.
There were impressive debuts for Craig Morgan and Liam Powell, while Bournemouth's Brian Stock was outstanding in midfield.
Wales made a bright start, and the Finns resorted to some rugged tactics to keep their hosts at bay.
Full-back Marco Parnela was booked on 23 minutes for a wild slash at David Pipe's legs, seconds after the Coventry player had been felled when the ball hit him straight in the face from a yard.
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