Neither player managed a break in the second set, and Nadal trailed as Dimitrov took some big rallies en route to taking the top seed into a tiebreak.
In the quarterfinals, Nadal will meet the iron with the Bulgarian Grigor Dimitrov, who defeated American Sam Querrey 6-3, 7-6 (3).
World number five Cilic secured his place in the semi-finals with a routine victory over Spain's Albert Ramos-Vinolas.
The 19-time Grand Slam champions faces either Richard Gasquet in the next round after he overcame fellow Frenchman Gilles Simon 7-5 6-7 (5) 6-3.
Cilic, bidding to reach the season-ending ATP Finals in London, grabbed the critical break in the sixth game of the first set on his way to a comprehensive victory.
Earlier, Marin Cilic, ranked fourth, showed the exit to the American Steve Johnson 7-6 (1), 6-4. It was another solid performance from him today, firing 10 aces and saving 3 out of 4 break points to limit the damage in his games.
World number nine Dimitrov had the first break-point opportunity in the second game, but Nadal denied the Bulgarian and the Mallorca native was punching the air after unleashing a blistering forehand victor to go a break up at 5-4.
The Swiss great, eyeing a second Shanghai Masters title, broke in the first game of the match and twice in the second set to march into the last eight.