Last spring, she won the Champions League with her Turkish team Vakifbank after defeating Conegliano in the final.
Two weeks later, Haak announced that she would switch to Conegliano for this season.
The 23-year-old from Ängelholm has previously had a trip to Italy.
In 2017-19 she played for Scandicci.
Conegliano beat Bergamo 3-0 in sets in the Italian league premiere.
Haak scored 15 points and was named MVP.
- It feels good to be back (in Italy).
There is a great atmosphere in the team and I am proud of how we played today, she said in the courtside interview.
3,613 spectators, flags and devoted fans, provided a tight framework in the arena.
A treat from the match was when Haak ended the first set with a delicious lob.