But Mourinho's changes allowed Chelsea to boss the midfield and also had an immediate impact in the final third.
Mikel played a pacy pass into Schurrle, who turned sharply before running purposefully towards goal and drilling a fine low cross-shot into the bottom corner.
Never go back?
Chelsea have already conceded more goals than they did in the whole of Jose Mourinho's debut season as Chelsea manager in 2004-05
It was the start of a lengthy spell of Chelsea domination, both in terms of possession and territory.
Ramires wasted several excellent shooting chances, Eden Hazard almost teed up Fernando Torres and Juan Mata shot straight at Asmir Begovic from the edge of the area.
The chances were not clear-cut but the visitors looked in control and Stoke, who had won just once in 11 previous games and had failed to score in seven of their 14 games, were barely threatening.
A tame Jonathan Walters header that went well wide of the post after a decent move was their only noteworthy attempt, however they managed to draw level by the break and took full advantage of Chelsea's failure to kill the game off.
Blues keeper Petr Cech hesitated as a long corner drifted into the box and was unable to recover his position in time to keep out Crouch's low strike.
Schurrle celebrates his first-half goal
Buoyed by their equaliser, Stoke started to show the belief and intensity they were missing before the break and their attacking intent was rewarded within five minutes.
But a Chelsea side well versed in fightbacks were level just two minutes and 21 seconds later when a venomous first-time half-volley from Schurrle flew into the net from 20 yards following a Mata free-kick.
Schurrle almost completed his hat-trick soon after, but his curled effort from the edge of the box smashed against the bar and to safety.
Simon BrothertonMatch of the Day commentator
"Chelsea dominated the first half and gained the early initiative and there only looked being one winner. But they could not make it count and Stoke earned the points with a fine comeback after a much-improved second half."
But Stoke, who had won only once in the league since August, were posing just as great a danger. Ryan Shawcross knocked a shot over the bar and Ireland should have scored from the angle of the box on the left, but shot wastefully over.
And with both sides leaving big gaps, Stoke broke forward and Assaidi, on loan from Liverpool, cut in from the right to score his first Premier League goal with a beautiful strike that found the top corner.
Chelsea slipped a place as a result, with Liverpool ahead of them on goal difference after a
4-1 defeat of West Ham.
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