Kokslien's wins move him up to third place in the season's World Cup standings, but still far short of France's Jason Lamy Chappuis, who holds a commanding lead in the table with seven events remaining.
Bernhard Gruber of Austria claimed his first podium position of the season, finishing in third place.
The event was the first to be held at the venue in the commercial capital of Kazakhstan, which was refurbished for the 2011 Asian Winter Games.