Genuine chances were few and far between during the opening 45 minutes.
Sandro could not extend Simon Mignolet with a bouncing shot from distance, and Gareth Bale was similarly wasteful when presented with a headed chance by Lennon.
Emmanuel Adebayor should have put the visitors ahead on the half-hour. Carlos Cuellar failed to cut out Jermain Defoe's curling shot, although he took the pace off it to allow Adebayor to get to the loose ball before Mignolet. However, the striker somehow managed to hit the bar from just two yards.
Cuellar looped a header over from Adam Johnson's free-kick, and it the Black Cats who took the lead two minutes later.
Neither Stephen Fletcher nor John O'Shea could make meaningful contact with Sebastian Larsson's free-kick as it sped towards goal, but after the Scot had seen his follow-up blocked by Hugo Lloris, O'Shea gleefully swept the ball home.
Sunderland's lead and optimism evaporated within six disastrous minutes. There was an element of fortune about Spurs' equaliser when Cuellar headed a 48th-minute corner into his own net, but things went from bad to worse just three minutes later.
Lennon attempted to lay the ball off, but saw it hit O'Shea and bounce back to his feet, and he raced in on goal to beat Mignolet.
Spurs should really have ended the game as contest on the hour when, with the Black Cats in disarray, Bale, who was later booked for diving, sprinted from halfway before picking out Defoe in front of goal.
The England striker had time to control before shooting, but as the entire stadium waited for the net to bulge, Mignolet pulled off a breathtaking save.