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.
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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.
Incredibly, the visitors were level seven seconds into the second period, with Sammy Ameobi, who entered as a substitute at the break, latching on to a clever Colback pass to finish past a stunned Hugo Lloris.
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Spurs had the chance to regain the lead after 53 minutes, but Eriksen's low effort was blocked by Fabricio Coloccini's last-ditch challenge.
Eriksen remained the main threat for the home team, but the Dane could not muster an attempt on target due to some stubborn defending from the visitors.
However, Spurs thought that they had an equaliser 20 minutes from time when Tim Krul bundled into his own goal, but the linesman raised his flag to indicate that the previous corner had drifted out of play.
The pressure from the home side continued in the latter stages, but clear chances remained at a premium as Newcastle held on a second league win of the season which takes them out of the relegation zone.