Prior to Tuesday's outing, Nigerian-American Pratt scored in Braga's opening 2-0 win over Sturm Graz and the winner in Saturday's 1-0 triumph over Apollon Limassol at the Arkadija Stadium.
In their final playoff tie, Barbara Azevedo, Francisca Cardoso, Vanessa Malho, Dolores Silva and Laura Luis scored a goal each to put Braga 5-0 up at half time.
After the restart, Pratt scored her third goal of the tournament and Braga's sixth goal of the night 15 minutes after she came on.
The emphatic win means Braga are through to the Round of 32 of the elite European women's club competition and become the second Portuguese side to achieve such feat after Sporting CP.
Braga's triumph ruined South Africa's Rhoda Mulaudzi's dream of reaching the next round with Apollon Limassol despite their 7-2 win over Sturm Graz on Tuesday.