The judges gave Malignaggi a unanimous decision, scoring the bout 116-111, 117-110 and 117-110.
“This is an emotional win for me,” said Malignaggi, who considered retirement after losing to Adrien Broner in June.
"This allows me to continue boxing. With a loss I don’t know if I would have wanted to continue. This big win puts me in the right spot in the talented welterweight division with a lot of money."
The 33-year-old victor looked far quicker throughout than an opponent three years his senior, but Judah complained that Malignaggi's negative tactics had robbed the bout of any interest.
“Paulie wasn’t tougher,” Judah said. “He didn’t want to engage and he stayed outside a lot. He kept working his jab and stayed on the outside. It just wasn’t there.”
At the same venue Shawn Porter earned a shock unanimous decision over Devon Alexander to claim the IBF welterweight title, with judges scoring it 115-113, 116-112 and 116-112 for Porter.
Also in Brooklyn, Sakio Bika clung on to his WBC super middleweight crown as his bout with Anthony Dirrell was judged a draw. One judge gave it to Bika, 114-112, another to Dirrell, 116-110, with the final judge making it 113-113.