Milos Raonic and Eugenie Bouchard each won their matches to give Canada a 3-0 victory over Italy in a group tie at the Hopman Cup on Thursday.
Canada now needs Australia to beat Poland with a clean 3-0 scoreline to move into the final of the eight-nation team event.
If the Poles win, they go through to the Saturday final and deny Canada a spot. Any other scoreline would lead to a count-back on games and sets won under the complicated tournament formula.
Montreal's Bouchard needed only 15 minutes on court for a 4-0 victory as Flavia Pennetta quit with right wrist pain to hand Canada a 1-0 lead.
Raonic, from Thornhill, Ont., hammered 10 aces and 21 winners in his 6-2, 6-4 win to keep Italy's Andrea Seppi winless over six matches and two editions in Perth. Canada won the mixed in a walkover due to Pennetta's injury absence.
The 23-year-old Raonic planned to watch the evening tie that will decide Canada's fate. He's pleased with his improving form as the Australian Open start approaches on January 13.
"I played much better today, it was night and day between today and my previous two matches," said Raonic. "I had to take matters into my own hands, that's something we've been working on. I took the initiative today.
"We are leading into a grand slam, and you want to make the most of every competitive opportunity."
Bouchard would have preferred to have played a proper match against Pennetta, who said that she woke up feeling poorly with the wrist pain, which she also felt at times last season when she returned to the WTA after surgery.
"It's disappointing not to play a full match, but Flavia was having problems," said Bouchard, 19. "I was excited to play.
"It's also tough to play an injured opponent, it can do things to your game. But I was playing with confidence, I believe in my game and am confident. I feel good, I've had a good start to the year."
Bouchard was playing for the first time since Canada's last group match Sunday.
On her one of days off, she visited a horse show and also advised Raonic against going swimming with non-lethal sharks in the city aquarium, which he did anyway in a publicity effort for the event.
The 32nd-ranked Bouchard had previously beat Australian Samantha Stosur and fell to Pole Agnieszka Radwanska prior to the Pennetta result.