The Canadian, 258th in the WTA rankings, produced a nerveless display to win 7-5 6-3 against an opponent ranked 43.
Only when victory was within her grasp did Stakusic wobble as four match points went adrift as Trevisan served at 2-5.
But she shrugged off that disappointment and powered through her next service game, ending the contest with a crunching off forehand winner.
"I'm so happy and honoured that I could play this week, this has been the best week of my life," Stakusic, who did not even play a WTA main draw match this year, said on court.
Canada have never won the women's team event, formerly known as the Fed Cup, or made the final but are now on the cusp of an historic triumph.
Former U.S. Open runner-up Leylah Fernandez, who has been in dazzling form this week including in a superb semi-final win against the Czech Republic, can seal the deal for Canada if she beats Jasmine Paolini in the second singles.
Should Paolini win it will go to the deciding doubles match.
