For all the noise and wall of flags that greeted their arrival, Spurs needed an early goal to feel at ease in their new surroundings.
It was Chelsea, though, who made the breakthrough against the run of play on 23 minutes when Alonso thumped home a superb free kick from 20 metres after Dele Alli had fouled David Luiz.
The shock jolted Spurs who spent much of the game peppering Chelsea's goal, with Harry Kane hitting the post and Christian Eriksen also going close.