Stephen Ireland struck shortly after the restart, but Schurrle's second goal of the afternoon looked to have secured a share of the spoils for the West Londoners.
However, Liverpool loanee Assaidi struck in the last minute of the 90 to seal the victory for the home team.
Below, Sports Mole has looked back over the clash to determine if the result was a fair one.
On target 3
On target 6
Was the result fair?
Even with the scores level at the break, Chelsea had been so dominant that it looked as though only one side was going to win this contest. They took their foot off the pedal somewhat in the second half, though, and Stoke punished them. Neither goalkeeper was overly busy so it could be argued that a draw was the fairest result, but credit should go to Stoke because they made the most of their chances.
Whatever Mark Hughes said to his players during the 15-minute interval, he should bottle it up. His side were poor in the first half, particularly in possession of the ball. It was as if a totally different team had taken to the pitch after the restart. They refused to allow Chelsea time on the ball and actually started to create some dangerous openings of their own. They would probably have taken a point before this game got underway, but to win it in such style will no doubt be a big lift to the Potters.
The Blues were so comfortable during the first half that it may actually have ended up being their downfall. They came out for the second half and appeared to be rattled by Stoke's change of attitude. At 2-2, they saw plenty of the possession, but they didn't call Asmir Begovic into real meaningful action. The biggest concern for Jose Mourinho will be the fact that his side have conceded six goals in their last two away matches against Sunderland and Stoke. With the greatest of respect, they are not teams that make a habit of scoring a lot of goals.
Sports Mole's man of the match
Peter Crouch: It's never easy playing as a lone striker, particularly when your outfit does not have too much possession. It means that when they do, it's vitally important that the frontman holds the ball up well and brings his teammates into play. Crouch did that today and caused the likes of John Terry and Gary Cahill problems whenever he could. His goal rounded off a good afternoon's work for the former England international.
Had this game ended level, Stoke's Ireland may have scooped this unwanted award for a bad miss. However, as the home side won, we will hand it to Chelsea goalkeeper Petr Cech. His side were cruising at 1-0 up when he came to collect a cross and got nowhere near the ball. After that, Crouch pounced and drew his team level.
Tempers flared towards the end, but to be fair to Jonathan Moss he dealt with it well and produced the yellow card when it was necessary. Chelsea may feel that he should have awarded a foul during the move that resulted in Stoke's second goal, but it is a debatable decision. Overall, it was a solid display from the man in the middle.
Stoke: Next weekend Hughes will come up against his former Manchester United teammate Steve Bruce when his side travel to Hull City.
Chelsea: The Blues are in Champions League action on Wednesday night when Romanian outfit Steaua Bucharest visit Stamford Bridge.