The unbeaten American was given the fight by scores of 117-111 and 115-113 on two judges' scorecards, while the third gave it to Malignaggi 115-113.
Broner, who had never gone beyond 10 rounds before, was stepping up two divisions from lightweight to take on Malignaggi in his home city of New York.
He said: "It's a tremendous accomplishment. Who's doing it like me in the game? Nobody."
Malignaggi showed plenty of grit and determination at Barclays Center but was ultimately outworked by his 23-year-old opponent.
"Paulie fought exactly how I thought he was going to fight - once he saw my power, he got on his bicycle, and I had to cut him off the whole fight," Broner said.
"I didn't have to use my footwork. He ran. All I had to do was cut off the ring. He couldn't hit me. He was shadow boxing."
Malignaggi, who was defending the belt he won just over a year ago, was incensed with the decision, saying as champion he should have been given the nod following a close contest.
"That was disgraceful. This was a close fight. The fight could have went either way. I don't think he did enough to take the belt from the champion tonight," he said.
"I'm not saying it was fixed, but the politically more connected fighter always gets the close decisions."