The Spaniard was asked plenty of questions by his Czech opponent, but consistently had the answers as he broke twice in each set to win.
Stepanek's pluck and exotic shot making - not least in managing to win a point by first getting to a seemingly impossible net cord, then returning Nadal's through-the-legs shot - earned him warm support from the crowd, as well as several chances to break Nadal.
But on the key points the world number two was always untouchable as he earned a fourth-round clash against Japan's
Nishikori shrugged off injury problems during a comfortable 6-4 6-2 win over the Czech Republic's
The number 13 seed took an injury time-out shortly before racing into a five-point advantage in the opening set tie-break, eventually holding off the Austrian 7-5.
And the Frenchman held off the pain better than Melzer could hold off his growing frustration during the match, recovering from a break in his serve early in the second set to double-break en route to the match.
Murray had received a walk-over into the fourth round after Canada's Milos Raonic pulled out of their round-of-32 tie hours beforehand due to an ankle injury.
And Simon has 48 hours to get his back closer to 100 per cent and prevent the prospect of a second bye for the Scot.
The Bulgarian rattled his Czech opponent in the first set, but looked to have peaked too soon when Berdych made short work of the second set.
But an engrossing decider remained dead level after eight games until Dimitrov broke the serve of his opponent with crucial timing before wrapping up a massive victory from deuce.
He will now meet