The home side had a fairly strong penalty shout inside two minutes when Steven Taylor appeared to handle inside his own box, but the referee was not interested and play continued.
Newcastle's best chance fell to Jack Colback after 16 minutes, but his low effort was wide of the post.
The home side were ahead two minutes later, however, when Adebayor headed a Ryan Mason cross into the back of the net.
It might have been 2-0 moments later, but Danny Rose fired high and wide after good work from Eriksen.
Spurs continued to dominate possession in the latter stages of the half, but clear chances were few and far between, with Newcastle unable to register an attempt on target in the first 45 minutes.