Emmanuel Adebayor's late goal sent Spurs into fourth spot above bitter rivals Arsenal although they have played a game more than Arsene Wenger's side.
Clint Dempsey cancelled out Steven N'Zonzi's opener with Charlie Adam seeing red for Stoke as Spurs ensured the chase for a top-four finish and a place in next season's UEFA Champions League will go down to the final day of the season.
Villas-Boas was deighted with his players and hopes Arsenal will slip up in their final two games so that Spurs can finish fourth.
"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," said Villas-Boas.
"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."
Villas-Boas singled out Dempsey for special praise after the American scored a superb 20th minute equaliser to cancel out N'Zonzi's early strike, then played a crucial role in Adebayor's crucial winner.
"He (Dempsey) has been absolutely immense this season with his assisting and his goalscoring and he has sometimes not got the credit he deserves," added Villas-Boas.
"He is a hard worker and a very complete athlete and he had an amazing game. It was an extremely good individual performance.
"We came back from difficult circumstances because part of Stoke's strength is their delivery at set-plays and the delivery (for the goal) was absolutely amazing.
"But we managed to control the other ones and the circumstances turned for us. I am extremely happy for the team in the way we were patient in the game, we kept the ball moving and eventually we got the breakthrough."