The world No 16 outplayed Bouchard 6-0 6-4 to give the Czechs a 1-0 advantage, before the 27-year-old returned to court a couple of hours later to win the deciding mixed doubles ??? which also featured Bouchard.
In between, Canada levelled the contest at 1-1 when Vasek Pospisil overcame Adam Pavlasek 7-6 (7-5) 6-2.
And after Safarova had teamed-up with Pavlasek to beat Pospisil and Bouchard 6-4 6-2, she admitted: “It’s the best way to start a season I could imagine and I started really strong.
“I had a really hard and good off-season in Florida and another week at home in the Czech Republic and then I came here. It’s the fifth day here, so I’ve had time to adjust to the hot conditions.
“I was going for all my shots (against world No 7 Bouchard) and it worked well. I tried to keep the pressure on, quickly. When she has time, she takes control so I??pressurised her from the first point.”
This year???s Hopman Cup will see world No 1 woman Serena Williams partner John Isner for the United States, while Andy Murray and Heather Watson make up a British team.
Great Britain open their campaign against holders France on Monday, the same day that the Americans take on Italy and Williams is hoping her week in Perth will help her to prepare for the forthcoming Australian Open later this month.
Temperatures in Perth are expected to reach 41 degrees Celsius and the 33-year-old said: “If anything it’s going to help me for Melbourne.
“Perth is one of the hottest places I’ve ever played, so it will be really good for the preparation in Melbourne, which is always super-hot.”?? ?? ?? ?? ?? ?? ??