Adebayor poked home a Clint Dempsey cross in the 83rd minute to earn his side a 2-1 win after Dempsey had cancelled out a third minute opener from Steven Nzonzi for Stoke.
Spurs had struggled to fashion a breakthrough despite dominating after Charlie Adams' 47th minute sending-off, but Adebayor's strike lifted them back above north London rivals Arsenal, who play their game in hand against Wigan on Tuesday.
Villas-Boas said: "It keeps us in the frame and gives us the possibility of making the Champions League so the important thing is the dream is still alive for us.
"We wanted to take it to the last day when we are playing at home, so it was an extremely important win for us for those reasons, and hopefully someone else will slip up. Arsenal are strong and experienced but it will go down to the wire."