Świątek, who was recently voted European Athlete of the Year, won 6-1, 6-3 at the Pat Rafter Arena in Brisbane, public broadcaster TVP Sport reported.
Poland’s world No. 1 told reporters after the match: "I'm pretty happy with my performance.”
Światek, who is also the WTA Player of the Year, added: "First matches of the season are always rusty. I was happy that in the important moments I was really composed."
Her victory over Putintseva gave No. 2 seed Poland a 1-0 lead over Kazakhstan in Group B of the United Cup, news outlets reported.
Later on Saturday, Poland’s Daniel Michalski lost 6-7, 2-6 to Timofey Skatov, making it Poland 1, Kazakhstan 1 after the first two matches of the tie.
Meanwhile, Świątek’s next game is on Monday, when she will face Belinda Bencic of Switzerland, Poland’s other opponents in Group B.
The Polish team is co-captained by former world No. 2 Agnieszka Radwańska and Dawid Celt, reporters were told.
The United Cup
The United Cup is a new mixed-teams event featuring 18 countries, who battle it out in the Australian cities of Brisbane, Perth and Sydney, WTA said.
The ties are played over two days, comprising two ATP and two WTA singles matches and one mixed-doubles match, according to officials.
(pm)
Source: TVP Sport, wtatennis.com, unitedcup.com