The 28-year-old won 115-111 113-114 115-112 on the judges' cards to claim the WBA, WBO, and IBF belts.
Lopez was knocked down in the first at Madison Square Garden while Kambosos was sent to the canvas in the 10th.
"I believed in myself, I backed myself," said Kambosos, who like the 24-year-old ended bloodied and bruised.
Kambosos, who has now won his last three fights by split decision, added: "I thought, 'I'm going to hit him hard and put him down', and the fight changed off that (knockdown). I'm an unbelievable boxer. I can't believe how good I boxed."