Alexis Sanchez snatched a point with the equaliser for Arsenal 14minutes from time after Tottenham had come from a goal down to lead 2-1 following the sending-off of Francis Coquelin.
The result left Spurs still second, two points behind leaders Leicester, who play at Watford later on Saturday, while Arsenal stay third, five points off the pace.
Manchester City closed to within two points of Arsenal after hammering bottom side Aston Villa 4-0 while Bournemouth look almost safe after winning 3-1 at second-bottom Newcastle.
"It's true that at 2-1 for us, 11 against 10, I have to be disappointed at the final whistle," Tottenham manager Mauricio Pochettino said after a pulsating clash at White Hart Lane.
"But I think we need to be pleased and happy because we kept the three-point (gap over Arsenal) and I think we played better than them.
"I think we are in a good position, we have many games and we need to be focused now."
- DPA