The Eagles took the lead in first-half stoppage time through a penalty from Connor Wickham, his first goal for the club, after Glenn Whelan had fouled Wilfried Zaha.Another penalty gave midtable Stoke the equalizer when Bojan Krkic converted after Damien Delaney handled inside the area.
But South Korea winger Lee secured the points for the visitors with a superb shot from distance.
Palace is unbeaten in four league matches in what could be a breakthrough season in Alan Pardew's first full campaign back in charge. His team is sixth with 29 points from 17 games, behind Tottenham and Manchester United on goal difference only.
It was the first game for Palace since confirming Friday a long-awaited deal with American sports tycoons David Blitzer and Josh Harris, who co-own the NBA's Philadelphia 76ers and the NHL's New Jersey Devils.
The duo, which had been in talks with the London club for more than a year about buying a stake, will join chairman Steve Parish in control at Selhurst Park.
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