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 half-time from the hosts put them ahead.
Peter Crouch and Stephen Ireland netted for Mark Hughes' side but their lead was soon wiped out as Schurrle grabbed his second in the 53rd minute.
However, Chelsea were 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 hosts, while Jon Obi Mikel and Schurrle were recalled in place of Frank Lampard and Willian for Mourinho's side.
The visitors 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 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.
Juan Mata nearly doubled the visitors' lead on their next attack, as 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 they grabbed an equaliser 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.
Their 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.
