Garcia sent Khan to the canvas in the third round with a left hook, but the 2004 Olympic silver medalist for Britain was able to beat the count.
At the start of the fourth, though, Garcia swarmed him with power punches, knocking him down twice quickly.
Khan got back to his feet each time, but the referee ended the bout at 2:28 of the round.
The American now has the WBA title to go along with his WBC one.
On the undercard, Fernando Guerrero beat Jose Medina by unanimous decision and Phil Lo Greco, J Leon Love, Daquan Arnett, Jamie Kavanagh and Abner Cotto won their bouts.