A sensational Icardi volley and injury-time Vecino header stunned Spurs in the San Siro
Inter completed a dramatic late turnaround as Matias Vecino headed in from close range in stoppage time.
Spurs took the lead eight minutes into the second half through Christian Eriksen.
The Denmark midfielder's first effort from the edge of the box was pushed away by Samir Handanovic but from the rebound Eriksen's deflected effort looped over the Inter goalkeeper and into the net.
Tottenham were punished for wasting a number of second-half chances as Mauro Icardi equalised for Inter with four minutes left.
The striker brilliantly volleyed in from the edge of the area from Kwadwo Asamoah's left-wing cross.
Spurs were unable to respond and suffered a third straight defeat for the first time under Pochettino.