John O'Shea had given Sunderland the lead just before half-time, but Lennon netted a solo effort as Spurs hit back in the second-period with two goals in a frantic three-minute spell.
Emmanuel Adebayor spurned an early opening for Tottenham when he scuffed the ball at Simon Mignolet, while at the other end Craig Gardner's deflected free-kick failed to trouble Hugo Lloris.
There was plenty attacking intent from both sides and Adam Johnson's dangerous cutback was cleared by Michael Dawson before Mignolet almost made a mess of a low shot from Sandro.
Spurs twice went close within a few minutes as Adebayor saw his shot blocked by Mignolet after racing clear and Gareth Bale then nodded narrowly wide.
Adebayor endured more frustration when he somehow blazed against the bar from a few yards out following Carlos Cuellar's clumsy attempt to cut out Jermain Defoe's cross.
Sunderland made the most of this reprieve in the 40th minute as Tottenham's failure to clear Sebastian Larsson's free-kick allowed O'Shea to stab the ball home.
But the happy hosts were soon deflated in the second period when Cuellar (48) needlessly nodded a corner into his own net after an aerial clash with team-mate Gardner.
A fine individual goal from Lennon (51) then stunned Sunderland as he left O'Shea in his wake with a lightning burst of pace and prodded the ball past the onrushing Mignolet.
Johnson tried to hit back with a low drive that was pushed away by Lloris, but the normally deadly Defoe then had a moment to forget, shooting too close to Mignolet after a fine run and cross from Bale.
The Welsh wide man was felled in the box by Gardner in the closing stages, but he was left bemused when the referee booked him for simulation instead of awarding a penalty.
Adebayor's finishing was yet again at fault soon afterwards when he burst into the box and fired at Mignolet, but Kyle Naughton was forced to make a timely interception as Sunderland searched for a late leveller.