Andre Villas-Boas' men had laboured in search of a potentially lucrative winner after Stoke midfielder Charlie Adam was dismissed in the 47th minute for a second bookable offence.
But Adebayor tapped in a cross from Clint Dempsey from close range in the 83rd minute to take them back up to fourth after Dempsey had cancelled out Steven Nzonzi's opener.
Source: PA
Source: PA