It is the fourth time Spurs have been held at their temporary home in the Premier League this season and Mauricio Pochettino's side lie fifth, three points shy of Liverpool a place above them.
Spurs almost lost in show-stopping fashion when defensive midfielder Obiang was allowed room 30 yards from goal to unleash a thunderous 70th-minute shot into the top corner beyond a helpless Hugo Lloris.
It was West Ham's first shot of any description in the game and, given Spurs had managed 20 by the time they fell behind, a share of the spoils was the least they deserved.