Cuban-American Quillin, who was born in Brooklyn, knocked N'Dam down six times on his way to earning the verdict 115-107 from all three judges.
The win improved his record to 28-0, while N'Dam was suffering his first defeat in 28 bouts.
Quillin, 29, decked N'Dam twice in the fourth, sixth and 12th rounds in the first world title fight without an interim tag for the Frenchman.
N'Dam bravely got to his feet each time after receiving punishing shots in the fourth and sixth rounds and was taking the fight to Quillin in the later rounds until he was floored twice in the final 30 seconds.
"I hope I inspired people that hard work can get you anywhere in life," said Quillin. "I'm very happy with this moment. I'm glad to be a world champion."