Tennis: Andy Murray reaches Shanghai Masters semi-finals
He was forced to overcome some worrying moments against Stepanek before hitting top gear to remain on course for a third successive Shanghai Masters title.
Murray was in trouble in the fifth game, conceding three break points and finding the net on the third, and never recovered as the confident Stepanek took the opening set with ease.
Their fortunes reversed in a hard-fought second set with Murray looking more comfortable and capitalising on a double fault to break in the sixth.
A stunning forehand winner - executed at full reach having dashed the width of the court - in the third game of the deciding set helped Stepanek secure a crucial break.
But Murray broke back immediately in impressive style and barely broke sweat as he cruised to victory, Stepanek buckling beneath the pressure in the closing stages.
Murray was satisfied with the way he finished the quarter-final but admitted Stepanek had caused him problems.
"It was quite a scrappy first couple of sets, but obviously in the second set I managed to get a break and got a bit of momentum," Murray said.
"I started going for my shots and dictated a majority of those at the end of the match.
"Obviously I needed to do that because he was playing with a lot of variety, making it hard.
"I was a little bit tentative on some shots. I allowed him to come forward."