Yes, they were gifted the lead when Kolarov hacked a Danny Rose cross into his own net in the ninth minute with a spectacularly bad piece of defending.
But Tottenham were well on top. They snapped into every tackle, hardly allowing City to catch a breath. Victor Wanyama was a tank. Heung-Min Son a terrier up front.
Christian Eriksen fizzed a free kick inches wide. Hugo Lloris saved one from Sergio Aguero.
The Lane erupted when Son took advantage of confusion in the City defence to slip Alli in on goal in the 37th minute, and the England man made it two.
Whatever Guardiola said at half time, he was quickly shaking his head again as shots from Son and Wanyama went whistling past the post.
City knew they had a mountain to climb. They had never come back from two goals down at half time to win in the Premier League, losing on 47 out of 48 occasions.