The Black Cats took the lead against the run of play when John O'Shea pounced to score his first goal for the club five minutes before the break after keeper Hugo Lloris had parried Steve Fletcher's shot.
However, the advantage lasted fleetingly as Spurs emerged for the second half and took the game by the scruff of the neck.
They were level when Carlos Cuellar headed Kyle Walker's 48th-minute corner into his own net and they forced their way ahead three minutes later when Aaron Lennon went one on one with keeper Simon Mignolet and came out on top.
That Lennon's strike proved decisive was testament to the resilience of the Belgium international, who produced a stunning second-half save to deny Jermain Defoe and was similarly stubborn when confronted by Emmanuel Adebayor, who had earlier been guilty of a glaring close-range miss, eight minutes from time.
O'Neill said: "We played with a lot of commitment and a lot of heart. We got ourselves in front just before half-time and it was obviously disappointing to concede two goals within two minutes.
"It knocked us back and while we were trying to press Tottenham obviously had chances to make it three but right until the end we kept going, so I couldn't fault the commitment of the team at all."
Meanwhile, Spurs boss Andre Villas-Boas confirmed defender Danny Rose is likely to remain at Sunderland on loan for the remainder of the season but that a permanent transfer is out of the question.
He said: "Permanent is completely impossible because we have big expectations for the player for the future, but there is a high possibility that his loan spell will continue."