Murray, fighting his way back to full fitness after 11 months away from the game following a hip operation, went down 6-4 6-4.
Edmund’s hard hitting proved a step too far for Murray, playing only his third match since his return.
“It was a tough match mentally,” said Edmund. “I’ve looked up to Andy so much, he’s always looked after me and I was nervous going into the last game. I played a solid match with some good tennis and I’m happy to get through.”
Edmund, who reached the semi-final of this year’s Australian Open and has replaced Murray as the British No 1, will face Mikhail Kukushkin in the quarter-finals after the Kazakh world number 90 surprised sixth seed David Ferrer 6-2 6-0.
Fellow British player Cameron Norrie will join Edmund in the last eight following his 6-4 6-3 win against Jay Clarke.