Kroell finished the race seventh and edged Feuz, who came second behind race winner Aksel Lund Svindal, by only seven points. Cuche, who will retire after the season, failed to score points in 17th.
"This is definitely the biggest achievement of my career," Kroell said. "It's fantastic to get this result here with so many fans supporting me."
Svindal, a former overall champion from Norway, finished the 2.9-kilometre Planai course in 1 minute, 46.82 seconds. Feuz was 0.57 behind, and Hannes Reichelt of Austria was third, 0.67 behind.
The top Canadian was Calgary's Jan Hudec in eighth. Ben Thomsen of Invermere, B.C., was 10th and Erik Guay of Mont-Tremblant. Que., 13th.
Guay finished seventh in the downhill standings while Hudec was ninth and Thomsen was 15th.
"We finished the year with three guys ranked in the top 15, which is great," Canadian head coach Paul Kristofic said. "Ben essentially came in unranked and ended the year top 15. For the second half of the downhill season he’s been stellar and Jan has been consistent every race. Erik, for sure, was a little disappointed but he will try to come back stronger next year."
Guay was disappointed by his 13th-place finish Wednesday.
"I wish I would have done better but that’s life," he said. "(The conditions were) pretty warm again. If you are on track everything’s good but as soon as you make a little mistake . . .
"I had two mistakes that cost me quite a bit," added Guay. "I didn’t ski well enough to be on the podium but could have maybe been top five (without the mistakes)."
Hudec was also frustrated with his result Wednesday, but after spending last summer battling a back injury, he was pleased with his overall performance this season.
"If you had told me at the beginning of the season that I would finish and in the points, well, I’m pretty stoked with that," said Hudec. "Today was super frustrating but I finished the season strong. You can nit-pick but I’m pretty pleased with how the season went."
Kroell, who led the downhill standings for the first time in his 14-year World Cup career, started the race 48 points clear of Cuche and 51 ahead of Feuz.
Last season, Cuche overtook leader Michael Walchhofer of Austria in the final race but never came close to repeating that feat.
The Swiss standout made a couple of untypical mistakes early in his run and almost skied out shortly afterward. He lost balance and avoided falling by pushing up with both hands on the snow before finishing 2.55 seconds behind Svindal.
"That surely was not the farewell I hoped for," said Cuche, who missed out on his final chance to match Austrian great Franz Klammer's record of five career downhill titles.
"I didn't start well and after that, it was hard to get going," Cuche said. "Congratulations to Klaus, he is a deserved winner."
Kroell said he was not aware of Cuche's result when he went down the course. Kroell struggled with the soft snow during Tuesday's training run and seemed to lack speed in some sections during the race as well.
"I first thought I had blown it all," Kroell said. "I had the sixth time at that moment and that would not have been enough if Cuche had got a good result."
Feuz started immediately after Kroell and needed a win to overtake the Austrian in the standings.
However, Feuz was behind Svindal's leading time throughout and trailed the Norwegian by more than half a second. Feuz celebrated the result as if he had won the race.
"The pressure on me was immense," said Feuz, who extended his lead in the overall standings. "I had no idea what Klaus had done so I was just very happy with my result. Second place is a giant relief."
Feuz earned 80 points and now leads Marcel Hirscher of Austria, who skipped the downhill, by 135 points with three races left.
"Everybody keeps asking me about the overall, and I just try to get it out of my head and focus on my racing," Feuz said.
Svindal, who crashed during Tuesday's training run, put in a near-flawless run for his first downhill victory of the season.
"This was perfect," said Svindal, who is favoured to win the super-G title on Thursday. "It was important to be fast today so I am a bit more relaxed for tomorrow's race."
The win also means that Svindal still has an outside chance for the overall title, trailing Feuz by 199 points.
"I don't count on anything," Svindal said. "Both Beat and Marcel must make several major mistakes and I don't expect them to do that."
Max Franz avoided a crash while racing at more than 100 kph (62 mph) when he caught a bump and lost his right ski. The Austrian managed to slow down on one ski and used a safety net to stop.
— With files from The Canadian Press