Gareth Bale started for the hosts but could not inspire his side to victory in Cardiff as Andy King's opener was cancelled out in stoppage time as the Finns grabbed a draw
King's second international goal early in the second half looked to have secured a friendly win for Wales in Cardiff on Saturday, but Riski latched onto a fine pass from the impressive Roman Eremenko in injury time and finished clinically to thwart Coleman's charges.
There had been much speculation over Coleman's future as his previous contract was due to expire after this game, but he put pen to paper on a new two-year agreement this week.
Coleman, who had been linked with the vacant Crystal Palace job, would have been encouraged by Wales' second half display but Mixu Paatelainen's side refused to accept defeat.
Gareth Bale made welcome return for his first Wales performance since his record move from Real Madrid and he showed glimpses of his class.
Finland, and Eremenko in particular, also had their moments and Teemu Pukki almost put Finland in front in the first half when his shot hit the post.
In-form Arsenal midfielder Aaron Ramsey was ruled out with a virus as Coleman made five changes to the side that drew with Belgium last time out.
Eremenko was passed fit after recovering from a dental problem and he was one of only four players to retain their starting berths following last month's defeat to France.
The visitors were unfortunate not to be in front after 14 minutes, when Wales stood off Pukki in the penalty area and the Celtic striker almost made them pay only for his right-footed strike to rattle the post.
Wales were struggling to fashion clear goalscoring opportunities, but Bale flashed a dangerous cross across the face of the goal that somehow evaded everybody after 26 minutes.
Finland goalkeeper Lukas Hradecky was finally forced into a save 10 minutes before half-time when he kept out Hal Robson-Kanu's downward header, but the goal would not have stood as Ashley Williams was penalised for a push.
Bale then cut in from the right touchline at full tilt before unleashing a vicious left-foot shot from 25 yards out that was beaten away by Hradecky.
Wales looked far more dangerous after the break and they were in front after 57 minutes when King burst into the box to head home Robson-Kanu's cross from six yards out.
Finland responded and Wayne Hennessey got done well to palm away a shot from the lively Eremenko in the 62nd minute.
Bale made another opportunity for himself when he fired wide after 77 minutes but Finland had the final say at the death when Riski showed a good turn of pace to race clear and apply the finish after Eremenko had played him in.