The South Africans were in control for most of the match and made the most of errors by their opponents, although they will not be completely happy with the Poles' second try at the end of the first half.
Despite this mini-slump, Renfred Dazel's team stepped up a gear after the break to add three tries to their two from the first half for a solid win.
The match started with a mistake by Poland from the kick-off, and Ayanda Malinga didn't need a second invitation to score the first try of the match after only 17 seconds.
Three minutes later, following another Polish mistake, Mathrin Simmers went over and with Nadine Roos again adding the conversion, the South Africans were up 14-0.
Poland had their first real opportunity in the fifth minute and they showed great patience on attack, with Oliwia Krysiak going over in the left corner.
After the hooter, South Africa missed a lineout throw and a few tackles before Anna Klichowska went over in the same corner to make it 14-10 at the break.
That was Poland's last action on the scoreboard though as Tshiremba scored from the restart, punishing yet another mistake by the home team.
After Poland were shown a yellow card for a cynical foul, the ball was quickly sent wide to Tshiremba for her second try, which increased the SA lead to 10 points.
They didn't stop playing when the full-time hooter went and Patience Mokone could celebrate her first try on debut for the Bok Women Sevens team.
Their next game is at 15h04 against Czechia and the final pool game is tonight at 18h12 against Argentina, who won their pool opener by 31-7 against the Czechs.
The Springbok Women's Sevens team had an up-and-down start in their first two pool games of the HSBC SVNS Play-offs in Los Angeles on Saturday, beating Ireland by 12-7 before going down to China 26-12 in their second game.
Springbok Women's Sevens coach Renfred Dazel said they are still on track for their 2025 goal of qualifying for next season's HSBC SVNS.
It's not quite an open invitation, but it will be a case of the more the merrier for Springbok Women's Sevens forward Kemisetso Baloyi on Saturday at the Athlone Stadium in Cape Town.
The Springbok Women's Sevens claimed third place in the first leg of the World Rugby HSBC Sevens Challenger 2025 at Athlone Stadium in Cape Town on Sunday.
