Tsuper, 34, was not among the favorites going into the event, but she benefited from the controversial format that has been introduced into freestyle skiing events this year and emerged with the gold medal from a group of just four finalists.
Prior to these Olympics, Belarus had won a single gold medal. It has three in these Games and two of them came Friday.
Biathlete Darya Domracheva won the women's 15-kilometer race earlier in the day for her second gold medal of the Olympics.
Twelve skiers entered the first stage of the three-stage finals, with American Ashley Caldwell having turned in what wound up being the best score of the day in qualifying. Caldwell, however, was eliminated in the first stage of the finals when the field was trimmed from 12 to eight.
The second stage cut the remaining group to four and they were left to battle it out for the medals with their last run being the only that counted.
Tusper's effort was judged to be the best. She received a score of 98.01. There were four better scores posted during the previous phases of the event.
China's Xu Mengtao won the silver with a score of 83.50 and Lydia Lassila was third with a 72.12.
Tusper grew up in Ukraine and represented that country in the 1998 Olympics. She left Ukraine for Belarus in 2002 to train with her former coach.