Andy King's second-half goal looked to have given Coleman his fifth win as Wales manager in 15 matches only for Riski to level in the 92nd minute.
The home team, without in-form Arsenal midfielder Aaron Ramsey because of illness, deployed a 4-3-3 formation with the in-form Bale repeatedly switching flanks.
Finland made the brighter start with Celtic striker Teemu Pukki hitting the post after 15 minutes.
The let-off sparked Wales into life and Bale swung a dangerous corner in from the left that somehow evaded everyone and went out for a goal kick.
There was an air of expectation from the crowd every time Bale picked the ball up and a trademark run and cross down the left caused problems for Finland.
The Finns, who have not lost to Wales since 2002, missed a good chance when Roman Eremenko blasted a free kick over the bar at the start of the second half as both teams continued to lack quality in the final third of the pitch.
Coleman had every reason to cheer in the 58th minute as Hal Robson-Kanu delivered an inviting ball into the box and King finished with the aid of his shoulder.
Wales then switched off in stoppage time and Eremenko slid Riski through to score.
Having failed to secure a place at next year's World Cup in Brazil, both sides are now building towards Euro 2016 qualification.
(Reporting by Michael Hann; editing by Josh Reich and Tony Jimenez)
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