The Bolton fighter was handed the verdict 117-111, 117-111 and 115-113 on the three judges??? scorecards as he notched his fifth successive win and took his overall record to 31-3.
Two-time world champion Khan kept Algieri at bay for much of the fight, the American landing a strong combination early in the eighth round but unable to connect often enough to claim victory.
Algieri fell to 20-2 with his second defeat in a row, the other coming last November in Macau at the hands of Manny Pacquiao.
Khan said: “He came to fight, wanted to win, had his home crowd, but I came here to win.
“The crowd really fired me up the last three rounds when Chris really came at me hard.”
Khan has now set his sights on a showdown with Floyd Mayweather, who kept his unbeaten record by defeating Pacquiao earlier this month.
“Amir Khan wants to fight Floyd Mayweather,” he screamed in the ring. “I want that next. I’m number one World Boxing Council (challenger). He’s the champion. So let’s make it happen.”