Kilde clocked in at 2 minutes, 02.35 seconds, edging out France Johan Clarey by 0.35 seconds. Italy's Mattia Casse took third place, 0.42 seconds behind Kilde.
Clarey, who took part in his first race in 2003, is still chasing his first World Cup win.
"It was a bit bittersweet to see that I came ahead of Clarey ... He deserved a victory," Kilde told Norwegian broadcaster NRK.
Clarey said he was disappointed by the result, but had no plans to slow down.
"I tried my best, but I made a lot of mistakes today because my skis were really fast. I believed I could win, but I'm behind a monster," Clarey said with a smile.
Overall leader Marco Odermatt from Switzerland ended up in a split seventh place with American Travis Ganong, 0.92 seconds behind Kilde.
Odermatt is now 111 points ahead of second-placed Kilde in the overall standings, in a season that so far has been dominated by the two rivals.