Second-half goals from Lisa Evans and Leanne Crichton put an end to Poland's resistance, and also extinguished the visitors' hopes of qualifying themselves.
Scotland coach Anna Signeul described the performance as "solid", an accurate summary on a night when Poland were determined not to repeat the 4-0 loss in their home game.
They kept nine players behind the ball until falling behind to Evans' strike, after which they came out of their shell and created problems for the home side.
Two good saves in each half by Scotland captain Gemma Fay ensured there would be no upset, and also gave her team a fourth clean sheet.
Signeul said: "There are expectations on the players to perform at a high level all the time and that's not so easy to do, especially in must-win games.
"If we had scored from one of our two early chances there would have been more, but Poland are a good team and it's difficult to break down a side that is sitting in deep.
"Lisa had a fantastic finish and a great second half. We tried to get her in behind the Poland defence and she did that for the goal and the assist for the second. She's world-class now."
As Signeul said, Scotland had two good chances to take the lead in the opening 15 minutes.
Poland captain Marta Mika almost deflected a Leanne Ross shot past her own goalkeeper and then the Scots came even closer when Rachel Corsie's header from a Kim Little corner hit the bar and bounced over.
There wasn't much more to excite the crowd in an uneventful first half in which the Poles sat deep and frustrated the home side.
The game finally sprung back into life when a powerful Evans shot looked like breaking the deadlock, but goalkeeper Anna Szymanska did really well to touch it on to the bar.
At the other end Fay had barely been tested, but just before the interval she had to look sharp to turn Patrycja Bhicerzac's low shot round the post for a corner.
The Scots showed much more urgency at the start of the second half with Jo Love and Jenny Beattie having chances before Evans finally made the breakthrough. The Potsdam player was fed by Little and fired in a well-placed shot between the goalkeeper and the near post.
Forced to attack, the Poles nearly equalised in the 73rd minute when an audacious 35-yard attempt from right-back Aleksandra Sikora was tipped on to the bar by Fay.
The Scots kept the best for last with a fine goal from substitute Crichton. Little's low cross was turned back by Evans and the Glasgow City player ensured her side would claim all three points.