Lee was down in the first and third but recovered superbly and the unbeaten Quillin was knocked down himself before tiring in the closing stages.
Judge Guido Cavalleri handed Lee the verdict by 113-112, giving the Irishman six of the last seven rounds, while judge Eric Marlinski had it 113-112 for Quillin, and Glenn Feldman had it a 113-113 draw.
The fight had been due to be for Lee???s WBO middleweight title but it became a non-title fight when Quillin failed to make the 160lb limit at the weigh-in on Friday.
Quillin started much the better and sent Lee down with a ferocious right hook that landed square on the jaw 29 seconds before the end of round one.
He repeated the trick moments later but the referee ruled that the bell had sounded before the punch landed.
Lee then survived the second but he was down again in the third, hit by a right in the chest, having been unbalanced when Quillin stood on his foot.
However, Lee began to get the upper hand after that and, although there was swelling around his eye, the ringside doctor said he was able to continue.
And Lee then produced a trademark right hook to send Quillin to the canvas in the seventh.
The wilting American was also second-best in the next two rounds but managed something of a revival in the 10th, before Lee finished strong.
The Irishman tried hard to secure the stoppage he clearly felt he needed and ended up doing enough to claim a draw.
Lee said: ???It was a hard fight to score. He had the knockdowns, but I boxed consistently, especially down the stretch.
???He got me early, because I was being lazy. I understand, with two knockdowns, people felt he won the decision. I could have done better tonight.
???If my next fight is Peter Quillin, so be it. It should be in Ireland, because he has an Irish last name and maybe he can find some ancestors there.???
Quillin said: ???There???s a reason why judges are judges, they see it their way. I respect the decision.
???I???m grateful that I was able to get back up and fight. I came here to fight and I was able to go 12 rounds.???