Spurs had an early opportunity the open the scoring when Michael Dawson's long ball put Jermain Defoe through, but the striker put his shot over the bar.
Jamaica rallied though as Jermaine Hue forced Brad Friedel into a low diving save, and Keammar Daley later hit the outside of the post with another drive.
After the break substitute keeper Andre Blake denied Emmanuel Adebayor after the Spurs striker had been set up by Tom Huddlestone.
Moments later Blake parried a Gylfi Sigurdsson shot from outside the area before reacting quickly to tip the ball away from Mousa Dembele as he followed in for the rebound.
Hugo Lloris had to be alert to save at his near post from a Darren Mattocks shot before the rebound was scuffed wide.
At the other end Jan Vertonghen was denied by the legs of Blake after connecting well with a delivery from Benoit Assou-Ekotto.