An Andre Schurrle double was not enough for the Blues as the Morocco international scored a late winner for Mark Hughes' men to give the Potters all three points.
Jose Mourinho's first visit to the Britannia Stadium got off to the perfect start thanks to Andre Schurrle's ninth-minute opener, but two goals either side of halftime from the Stoke had the home team ahead.
Peter Crouch and Stephen Ireland netted for Mark Hughes' side but the lead was soon wiped out as Schurrle grabbed his second in the 53rd minute.
However, Chelsea was not able to hold onto the point as Assaidi fired a sensational effort into the top corner from 25 yards to record a memorable victory.
Both managers made two changes from their midweek fixtures as Marc Muniesa and Jonathan Walters replaced Erik Pieters and Assaidi for the home team, while Jon Obi Mikel and Schurrle were recalled in place of Frank Lampard and Willian for Mourinho's side.
The Blues had the first sight of goal after just five minutes but Ramires wasted an excellent chance, however, they did not have to wait long for the opening goal as Schurrle netted five minutes later. The Germany international jinked past Ryan Shawcross twice before rifling his shot low into the bottom corner from the edge of the penalty area.
Mata nearly doubled the lead on the next attack. A loose ball dropped to the Spaniard on the edge of the penalty area but his effort was straight at Asmir Begovic.
Stoke had struggled to make any impact on the game but grabbed an equalizer in the closing minutes as Chelsea failed to clear a left-wing corner. The ball was allowed to bounce inside a crowded penalty area, with Petr Cech coming halfway for the ball before backing out, and Crouch pounced to fire into the net.
Hughes' side took the lead early in the second half through substitute Ireland - his second goal for the club. Walters raced down the right and played the ball into Ireland, with the 27-year-old calmly curling a fine finish past Cech into the far corner.
The lead lasted a mere three minutes as Schurrle grabbed his second when Stoke failed to clear an Eden Hazard free kick, the 23-year-old thundering a first-time volley into the bottom corner from 18 yards.
Ireland had a fantastic chance to restore Stoke's lead in the 67th minute after superb work from Crouch, but the midfielder smashed his effort over the bar.
However, there was still time for late drama as Assaidi drifted in from the left and launched his effort beyond Cech and into the top corner, snapping a three-game losing streak against the London club and inflicting Mourinho's first ever Premier league defeat in the month of December.