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 clattered into the back of Wilfried Zaha's leg
Despite three fine saves from Wayne Hennessey, the Potters levelled from the spot themselves when Bojan Krkic converted after referee Robert Madley deemed Damien Delaney had handled inside the area
Alan Pardew's men would find a late winner, though, as Lee rifled a measured first-time effort into the far corner of Jack Butland's net from a semi-cleared corner.
Xherdan Shaqiri had overcame a hamstring injury to return to the starting line-up alongside Marko Arnautovic and Bojan as Mark Hughes named the triumvirate that had dismantled then leaders Manchester City two weeks earlier.
The Potters only needed to go past the three-minute point to mark 500 minutes without conceding in the top flight when captain Ryan Shawcross had been on the pitch.
At the other end, Shaqiri was experiencing a fairly nondescript afternoon - typified by a snatched shot that went well wide - but he and Stoke finally came to life when the Swiss danced beyond a couple of defenders before Delaney slid in to smother his effort.
Bojan drew Hennessey into a decent save, Ibrahim Afellay lashed an attempt high and wide and Stoke then struck the post as Erik Pieters' cross was touched on to the woodwork by Marco van Ginkel's prod.
The visitors, missing Yohan Cabaye because of a heel injury, had been quiet yet that all changed on the stroke of half-time when Whelan barged into Zaha's left leg in the area after the hosts had failed to clear a free-kick.
In Cabaye's absence, Wickham stepped up and drilled the stoppage-time spot-kick straight down the middle.
Hennessey continued to be the busier keeper after the break with a fine one-handed save to thwart Glen Johnson after the full-back had cut onto his left foot.
Palace's counter-attacking threat came to the fore once they had a one-goal advantage, though, and James McArthur's sliding effort almost went past Butland's body, while Marouane Chamakh, on as a substitute for injured goal-scorer Wickham, fired wide on another break.
Arnautovic, who moments earlier was unable to force home a scrappy corner, saw an effort deflected narrowly wide by Joel Ward's block and it looked like it might be one of those days for the hosts.
That feeling did not change when Madley did not give a penalty for a shove on Arnautovic, the ball breaking to Bojan, whose one-on-one try was saved by Hennessey.
However, Madley did point to the spot in Stoke's next attack as the ball came down and struck Delaney's hand from a header
Having just been denied by Hennessey, Bojan won the duel this time by sticking the penalty away to the keeper's right
Neither side looked content with a point, Shaqiri's free-kick dropping just wide and Butland denying Yannick Bolasie, and Lee won it with a controlled attempt past Butland after Glen Johnson's block had come out to the South Korean.
TWEET OF THE MATCH
Ben Bailey Smith (?@docbrown88) - " That's massive for Wickham
Needed that! #cpfc"
PLAYER RATINGS
Stoke
Jack Butland: 6
Glen Johnson: 7
Ryan Shawcross: 6
Philipp Wollscheid: 5
Erik Pieters: 7
Glenn Whelan: 5
Marco van Ginkel: 6
Xherdan Shaqiri: 6
Ibrahim Afellay: 6
Marko Arnautovic: 6
Bojan Krkic: 7
Substitutes
Jonathan Walters: 6
Charlie Adam: 6
Crystal Palace
Wayne Hennessey: 8
Joel Ward: 7
Damien Delaney: 6
Scott Dann: 6
Pape Souare: 7
Joe Ledley: 7
James McArthur: 7
Wilfried Zaha: 7
Jason Puncheon: 7
Yannick Bolasie: 8
Connor Wickham: 7
Substitutes
Lee Chung-yong: 8
Jordon Mutch: 6
Marouane Chamakh: 6
STAR PLAYER
Wayne Hennessey
Lee Chung-yong's fine effort won it but Palace were only it for so long because Hennessey made so many saves
He even almost got to Bojan Krkic's penalty.
MOMENT OF THE MATCH
Lee's winner
He looked like he know exactly what he was doing when the ball came into his path and he arrowed the try beautifully beyond a host of bodies and Jack Butland's despairing grasp.
VIEW FROM THE BENCH
Mark Hughes went with the three-pronged attack of Marko Arnautovic, Bojan and Xherdan Shaqiri once more but they failed to sparkle as they had done two weeks earlier
For Alan Pardew, it was a late substitute who won the game..
which is always pleasing for a manager.
MOAN OF THE MATCH
That the front three of Bojan, Shaqiri and Arnautovic was unable to shine in the same manner they had against Manchester City.
WHO'S UP NEXT?
Stoke v Manchester United (Barclays Premier League, Saturday, December 26)
Bournemouth v Crystal Palace (Barclays Premier League, Saturday, December 26)
Source : PA
Source: PA