Boro made a good start when Afonso Alves slotted into the corner, but the Brazilian’s strike was correctly ruled out for offside.
But Spurs took the lead after 27 minutes when Dimitar Berbatov’s flick and cross picked out Aaron Lennon and his volley struck the unfortunate Jonathan Grounds on its way in.
David Wheater saw a towering header cleared off the line by Lennon, while Berbatov saw a deflected shot hit the post.
But Boro stepped up the pressure and deservedly equalised on 69 minutes when Downing cut in from the left and fired a powerful right footed-shot which took a deflection off Jermaine Jenas.
Alves missed a great chance to win it late on when he broke clear but poked past the post.