The home supporters in the Swiss Alps were cheering for Rogentin and fellow Swiss Marco Odermatt (25) but saw Kilde push hard and win the race.
Kilde clocked one minute, 47.84 seconds, edging out Rogentin by 0.27 seconds. Odermatt took third place, 0.66 seconds behind Kilde.
"On the limit, that’s how we have to do it in super-G, and sometimes it works and sometimes not," Kilde said after the race.
Rogentin secured his first-ever World Cup podium.
"Special day for me, amazing feeling. It couldn’t be better," Rogentin said.
"That’s so special, my first podium and to share it with Oddie (Odermatt), that’s perfect."
Odermatt is now 360 points ahead of second-placed Kilde in the overall standings in a season that so far has been dominated by the two rivals.
