Khan, 26-3 (18 KOs), looked the superior fighter early on, showing vastly superior hand speed as he landed right hands behind a long jab and opened up a cut on Garcia's eye with a left hook.
Garcia's defense remained tight and effective, however, and in the third round began throwing thudding shots to Khan's body and near the end of the round he landed a powerful counter left hook that dropped Khan hard on to his back.
The Briton struggled to his feet, but was on shaky legs as the bell rang.
Garcia dropped Khan again at the start of the fourth with a right hand and as he retreated, Garcia gave chase, launching huge punches as he did so.
A left hand put Khan down once more, and although he beat the count, referee Kenny Bayless stopped the fight though the Briton thought the stoppage may have been premature.
"I was a little surprised the ref stopped it," he said. "I thought he was going to let us continue. My mind was clear, and I thought my legs were okay.
"(But) it wasn't my night. I respect Danny. He was countering very well against me. I got a little complacent and he took advantage and he caught me."
Garcia said he had felt the Briton had underestimated him.
Photograph: Jeff Gross/Getty Images