Tottenham won at Stamford Bridge for only the second time in the league for 36 years as 10-man Chelsea were beaten at home.
England midfielder Cole Palmer was also sent off in the 80th minute for two bookings to complete a miserable evening for Xabi Alonso's side.
Spurs had taken the lead three minutes earlier in fortunate circumstances.
Chelsea goalkeeper Mike Penders, on his first league start for the Blues after Emi Martinez suffered a fractured jaw against Everton, punched the ball into his own net when he jumped under pressure from Jan Paul van Hecke at a corner.
French forward Mathys Tel added a second in the 87th minute with a low strike from 25 yards out following a fine individual run from the halfway line.
The match was played in torrential rain and it was stormy on the pitch too in a fiery derby encounter.
Palmer picked up his two bookings in a nine-minute spell, either side of Tottenham's opener. His first yellow card came when he barged into Mateus Fernandes, with the second following a late challenge on Conor Gallagher.
Spurs moved up to 12th place, having won two matches in a week after they gained their first league victory of the campaign on Monday with a 3-1 home win over Coventry City.
As much as it was deserved, it was unexpected given their wretched record at the home of their London rivals.
Tottenham had won just one of their last 36 league visits to Stamford Bridge with 11 draws and 24 losses. The only previous victory in that run had come on 1 April, 2018 when Mauricio Pochettino's Spurs won 3-1 against a Chelsea side managed by Antonio Conte.
Before that, you had to go back to 10 February, 1990, in the old Division One when a Spurs team led by Terry Venables won 2-1 at Stamford Bridge against Bobby Campbell's Chelsea side.