Goals from Terrence Boyd and Branko Boskovic helped move Rapid a point behind second-placed Dynamo Kiev as they claimed their first win of the campaign.
The two teams meet in the final match in the group in Ukraine in two weeks' time.
Bottom side Thun, however, have no chance of progressing.
Thun briefly threatened to snatch an undeserved draw when Berat Sadik brought them level in the 61st minute, but Boskovic's winner came three minutes later and helped settle any home nerves.
Rapid made the breakthrough in the 17th minute when Boyd provided a low, close-range finish to Marcel Sabitzer's ball in from the left.
The hosts' lead looked comfortable throughout the rest of the first half as Thun rarely threatened.
And the Austrians continued to hold the upper hand in the second half, Christopher Dibon getting a shot away only to see it blocked by defender Fulvio Sulmoni.
Sabitzer then had a right-footed effort from the right tipped round a post by Guillaume Faivre.
Thun equalised against the run of play in the 61st minute as Sadik bundled home Enrico Schirinzi's ball across goal, despite mishitting his finish.
But Rapid were back in front three minutes later, Boskovic firing high into the net from Guido Burgstaller's cross from the right.
Dominik Starkl forced Faivre into a save with his feet as Rapid looked to extend their lead, but they had their own keeper Jan Novota to thank at the death.
Novota parried away a Sadik shot from inside the area to ensure his side held on to all three points.