Their crushing defeat by Borussia Dortmund over two legs in the Europa League showed how far they still are from the true European elite. But credit where it is due.
This game was all about how they would respond, and they couldn’t have made a better start, with Kane flicking home a Kyle Walker cross after just 44 seconds.
His second was laid on a plate for him by Dele Alli’s slide-rule pass, the midfielder’s 11th assist in all competitions, and finished with aplomb.
Kane turned provider later in the half but Alli was rightly flagged offside as he put the ball in the net.
Howe made changes at half time in a bid to get Bournemouth back in it, but Spurs went close again when Kane slipped in Walker and his shot whistled wide.
And it was game over when Artur Boruc could only parry a long-range shot from Kane back into the danger zone for Eriksen to prod home on the rebound.
The visitors kept plugging away but never really threatened a miracle comeback, and Spurs looked happy to see the game out.
Alli still managed to get under the skin of several Bournemouth players before it was over, but missed a great chance to make it four when he sliced Eriksen’s cross wide.
The England midfielder still got a standing ovation when he came off to be replaced by Ryan Mason at the end.
Spurs just need to wrap him and Kane in cotton wool, because if they keep playing like this there could be something much, much bigger to celebrate.