Despite pushing his opponent to three sets, Kyrgios failed to deal with American John Isner's serve, going down 6-3 6-7 (9-7) 6-3.
Nadal survived two break points in his opening service game, before winning the last five of the first set to assume control of his match against Bolelli.
The Spaniard carried that momentum into the second set by opening with a break of serve and made one further gain to add further gloss to the triumph.
Nadal will now meet Grigor Dimitrov - a man he has beaten in all five previous meetings - in the last eight after the Bulgarian saw off world number nine Stan Wawrinka with a 7-6 (7-5) 3-6 6-3 win.
"I know what to expect from him and we all know what I'm going to put out there on the court, which is going to be a great performance," said Dimitrov. "It's one of those days where I really want to be out there on the court, playing against him on clay.
"I feel like I have been playing good tennis, so why not go out there and have fun, but at the same time, I know why I'm out there."
Tomas Berdych defeated Jo-Wilfried Tsonga 7-5 6-2 to set up a quarter-final clash with Isner.