Gareth Southgate's men, who had begun a new World Cup qualifying campaign with wins over San Marino and Albania, just about did enough against a Poland side without the injured Robert Lewandowski.
The Three Lions were good value for their lead amid a commanding first-half display, Harry Kane becoming England's all-time leading penalty scorer on 10 as he converted after fine play by Raheem Sterling.
Stones gifted Poland a chance that Jakub Moder capitalised on in the 58th minute, though he played an important role as Maguire's goal maintain England's unblemished start in Group I.
England played the ball around with swagger during the early exchanges and almost opened the scoring in the eighth minute, only for Phil Foden to head Ben Chilwell's cross over after Mason Mount carved the Poland defence open.
Nevertheless, England did not have to wait much longer to take the lead, Kane confidently dispatching a penalty having seen the lively Sterling clumsily tripped by Michal Helik.
Kane was then denied a second just past the half-hour mark, latching on to Foden's clever first-time offload and forcing Wojciech Szczesny into an applaudable save down to his right from 20 yards.
England was pegged back before the hour, Stones – who had put England in trouble a few minutes earlier only to be bailed out by Nick Pope – was robbed just outside his own penalty and Moder applied an emphatic finish after being fed by substitute Arkadiusz Milik.
England's response was meek, the home side's urgency showing little sign of improvement as the seconds ticked away – Foden's weak right-footed shot in the 69th minute causing Szczesny no bother.
There was to be a final hurrah for the host side, however, as Stones made up for his earlier blunder by heading a corner delivery back into the danger zone and Maguire smashed past the helpless Szczesny to seal the points.