Spurs manager Villas-Boas saw his side take a first-half lead through Gylfi Sigurdsson, but in a frenetic and keenly contested second half, Chelsea equalised through John Terry before having Fernando Torres sent off.
The point nudged Spurs above Arsenal at the top of the table, while Chelsea climbed one place to third ahead of the rest of the weekend programme.
Sigurdsson gave Spurs a 19th-minute lead at White Hart Lane when he rode a challenge from Terry to gather Roberto Soldado’s lay-off before steering the ball past Petr Cech.
Juan Mata teed up the equaliser in the 65th minute with a free-kick that was headed home by Terry. Torres played well in the second-half, but having earlier appeared to scratch Jan Vertonghen in an off-the-ball incident, he was sent off in the 81st minute after being shown a second yellow card for a challenge on the same player