Second-half goals from Lisa Evans and substitute Leanne Crichton maintained Scotland's 100% record in Group 4 against a resolute Poland.
Group favourites Sweden had the better of the weekend, beating Northern Ireland 4-0 in Portadown, but remain three points behind Scotland with an inferior goal difference.
They have a game in hand, but do not play again until next month, whereas Anna Signeul's side play Bosnia-Herzegovina in Zenica on Thursday and could extend their advantage to six points.
Having lost 4-0 in Poland, the visitors set out their stall in an uncompromisingly defensive manner. They had nine players behind the ball for most of the first half, stifling Scotland's attempts to make an early breakthrough. In their recent Cyprus Cup matches Scotland prospered by finding space behind the defences of teams that, being higher ranked, were naturally looking to play attacking games themselves. Poland provided a very different proposition, and the heavy nature of the Fir Park surface was another factor which did the Scots and their quick passing game no favours.
It all added up to a frustrating opening 45 minutes, although Rachel Corsie, with a header, and Evans, from a shot, did have efforts which hit the woodwork, the latter touched on to the bar by Polish keeper Anna Szymanska. Against that, Scotland captain Gemma Fay also made two important saves, the first just before half-time and the other when the score was just 1-0 in the second half.
Glasgow City midfielder Leanne Ross, whose 100th cap against Chile in Brazil last December was marked by a presentation before the start, said: "All credit to her because it must be difficult for a goalie to maintain her concentration when a game is so one-sided. It was a difficult match.
"We beat them 4-0 away so they had a game plan to sit in a bit deeper which causes us a problem because we like to play in behind defences."
If much of the game was a battle of wills between the two sides, the Scotland goals stood out from the general context because of their excellence. Good work by Corsie and the game's best player, Kim Little, set up a chance for Evans; instead of taking the easy option of aiming for the far corner she fired a fierce shot into a narrow pocket between Szymanska and her near post.
The Potsdam striker also laid the ball back cleverly for Crichton, after Little was again the provider, for the goal which ensured the outcome nine minutes from the end.