Bill Koch of Putney, Vt., won the first official Nordic World Cup cross country ski title by capturing yesterday's 15-kilometer final event in Castelrotto, Italy.

Koch, clocked in 37 minutes 52.5 seconds, ended the season with 121 points. He finished 59.6 seconds ahead of Milos Becvar of Czechoslovakia in the final race and 1:04.4 in front of third place Harri Kirvesniemi of Finland.

Koch, 26, began the day with 92 points, third to the 114 of previous standings leader Thomas Wassberg of Sweden and the 102 of Kirvesniemi.

According to World Cup rules, Wassberg had to finish first or second to increase his point total, while Kirvesniemi needed a fifth or higher for more points. Wassberg failed to gain any ground and Kirvesniemi's four points for third place only boosted the Finn's total to 106.

Koch, 30-kilometer silver medalist in the 1976 Innsbruck Olympics and bronze holder over the same distance at the world championships in Oslo earlier this year, won the World Cup despite an illness that kept him out of a 50-km event this season. Under Cup cross-country rules, a skier may count a total of six races during the season to determine his overall point total . . .

In Sansicario, Italy, Andreas Wenzel of Liechtenstein won the experimental super giant slalom ski race and termed it "the best kind of race I skied in the last five years." Wenzel was timed in 1 minute 48.36 seconds in the final contest of the men's 1981-82 Alpine skiing season. Second, in 1:49.04, was Marc Girardelli, an Austrian who skis for Luxembourg.