Under crisp blue skies in Colorado, Austrian Kroell set a time of 1:41.52 on the famous Birds of Prey slope to edge out compatriot and rising star Max Franz, who was 0.45 seconds back.
Italy's Christof Innerhofer rounded off the top three.
Kroell went close to victory at last year's event at Beaver Creek, ending up third, a mere 0.14 seconds behind winner Bode Miller and Beat Feuz - both of whom are now struggling to return from knee injuries, with the latter out for the season.
Kroell knows he has a good chance of what would be a first victory at Beaver Creek for him, but is aware winning the first training run does not count for much in the final reckoning.
"It's of course good for your confidence,” Kroell said. “But, it says almost nothing about what might happen in the races.
"It’s good to do a good time but most skiers take it easier as there is less pressure on the first training. This is one of the rare occasions when you can hold something back, luckily others held back more than me.”
Kroell, 33, said he was impressed with the Birds of Prey course.
“I had so much fun, it was great," he added. "The slope was great and already after inspection I knew that it was going to be so much fun skiing down.
"Of course my experience helps me a lot, on the start, even before the inspection I know exactly the way I need to go – I know exactly what I have to do, with a 10cm difference here and there. I push out the start focusing on skiing well and finding the best line. Today it simply worked.”
Aksel Lund Svindal, who was imperious in victory at Lake Louise last weekend, came in fifth, 0.88 seconds off the pace.
"Svindal has been amazing in Lake Louise and I am definitely keeping an eye on him. After dominating those first two races we all know he is strong and I will have to push hard in order to beat him,” Kroell added.
Wednesday's second training run is scheduled for 10:45am local time (5:45pm UK).
Top 10 times
1 KROELL Klaus AUT 1:41.52
2 FRANZ Max AUT 1:41.97
3 INNERHOFER Christof ITA 1:42.13
4 STREITBERGER Georg AUT 1:42.31
5 SVINDAL Aksel Lund NOR 1:42.40
6 SPORN Andrej SLO 1:42.48
7 THEAUX Adrien FRA 1:42.68
8 GUAY Erik CAN 1:42.71
9 JANSRUD Kjetil NOR 1:42.75
10 CLAREY Johan FRA 1:42.91