The 28-year-old Khan consistently beat Alexander to the punch, jabbing his way to victory in the non-title fight on all three judges' scorecards, 120-108, 119-109 and 118-110.
Khan used his jab effectively to set up combinations that earned him the bulk of points as both fighters made it to the final bell.
Khan also showed off his much-improved defensive skills, the result of working with trainer Virgil Hunter as the two posted their fourth-straight win since hooking up in September 2012.
Alexander, who looked impressive in his last fight against Jesus Soto Karass, went into the 12th round needing a knockout to win.
Khan was originally scheduled to fight the American for Alexander's International Boxing Federation welterweight title last December in New York.
But the Briton scrapped the bout because he thought he had a chance at landing a bank-breaking dream bout with Floyd Mayweather that never came off.
Speaking to the media after his win, Khan said he trained very hard for this fight. “I knew I had to make a statement tonight; it was against a tough, very skillful guy, but it was one of my best performances, he said, according to a BBC report.
"I'm the best boxer and have the quickest hands in the world. I've just turned 28 and I'm getting better and getting quicker, I just had to become smarter,” he added.
"It's in my blood to fight, but today I was able to reset myself. I've got the best jab in the business."
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You are the champ!
Great !!!