An own goal and a second-half free-kick from Andriy Yarmolenko sealed a win which takes Dynamo four points clear in second place in Group E and within a point of leaders Genk.
The Ukrainians had every reason to travel in confidence having disposed of the same opponents 3-0 in their clash in Kiev last month.
But Thun clearly had other intentions and Christian Schneuwly got a shot on target in the first minute which forced alert Kiev goalkeeper Aleksandr Shovkovskiy to make his first save.
In an open start Mbokani brought a save out of Guillaume Faivre at the other end but Thun came within inches of opening the scoring in the seventh minute when an effort from Berat Sadik hit the woodwork.
Thun had started with confidence and their chances of claiming a vital win were boosted in the 17th minute when Mbokani was sent off for a foul on Lukas Schenkel.
Sadik twice missed the target as the home side tried to make their advantage tell, but they were stunned by a major error by Schenkel in the 29th minute when he turned a harmless-looking cross from Yarmolenko into his own net.
Kiev made the most of their reprieve and restricted their opponents to half-chances for the rest of the first period before almost extending their lead in the 50th minute when Yarmolenko fired wide.
Sadik missed an increasingly rare chance for Thun on the hour before the dangerous Yarmolenko put the game out of the home side's reach in the 69th minute when he cut a free-kick past Faivre.