France ended Finland's hopes of qualifying for the World Cup for the first time as a 2-0 win from the world champions ensured that the hosts finished in third place in Group D.
France had already secured their place at Qatar 2022 meaning the pressure was on Finland and Ukraine to battle it out for a play-off place.
Finland began the night in the box seat, two points ahead of Ukraine, but the situation was turned on its head in the second half.
Oleksandr Zinchenko and Artem Dovbyk secured a 2-0 win for Ukraine over Bosnia-Herzegovina while Karim Benzema's deflected strike and a superb individual effort from Kylian Mbappe saw the reigning world champions claim maximum points as Finland fell at the final hurdle to drop to third.
Benzema and Mbappe played a neat one-two and the Real Madrid forward's effort nicked off Leo Vaisanen and beyond Lukas Hradecky to open the scoring after the 66th minute.
Finland's goalkeeper was beaten again 10 minutes later, Mbappe burning Vaisanen for pace down the left and bending an unerring finish into the bottom-right corner.
Hradecky's brilliant save denied Mbappe a second, with the Paris Saint-Germain star's second-half performance illustrating the gulf in class that made sure Finland will watch next year's World Cup from home.