Meanwhile, sixth-seeded Tommy Haas withdrew late Thursday night, citing a respiratory problem that has plagued him all week. Haas' departure means Feliciano Lopez of Spain advances to the quarterfinals in a walkover.
In the other night match, Jack Sock defeated James Blake in a battle of wild-card entries from the United States, 7-5, 6-4.
Cilic, the world's 12th-ranked player, battled Sijsling for more than 2 1/2 hours and saved four break points in the 11th game of the third set to take a 6-5 lead. He squandered a match point with Sijsling serving at 5-6 in the third set.
Sijsling double-faulted on his third match point of the tiebreaker and lost when he netted a forehand from behind the baseline.
The win moved Cilic—who won his ninth ATP Tour title two weeks ago in Zagreb, Croatia—into the quarterfinals against fifth-seeded Kei Nishikori of Japan, who advanced with a 6-3, 6-3 victory over qualifier Donald Young of the U.S.
Also, Marinko Matosevic of Australia eliminated fourth-seeded American Sam Querrey 3-6, 6-4, 7-5 in a match that lasted almost two hours. Querrey had saved one match point in the deciding game, but double-faulted to send the advantage
Matosevic, ranked 53rd in the world, said he was pleased with his play after dropping the opening set. He said returning serve is one of his strengths, and despite Querrey recording 15 aces, Matosevic was able to keep some of his 135-mph serves in play "and win the rally."
"I started to return a little bit better, and probably the major thing was I picked up my serve percentage," Matosevic said of his play in the last two sets. "I started to get a few more free points and started to hold my own serve a little bit easier."
Also advancing were No. 7 seed Alexandr Dolgopolov of Ukraine, Denis Istomin of Uzbekistan and American Michael Russell.
Dolgopolov beat American qualifier Rhyne Williams 6-4, 4-6, 6-4; Istomin defeated former world No. 1 Lleyton Hewitt of Australia 6-1, 6-2; and Russell won 6-2, 6-4 over Lukasz Kubot of Poland.
Haas' withdrawal came as the day's matches moved late into the night. Three-set matches for Cilic and Querrey pushed the start of the evening matches well past their scheduled start. By the time the Sock-Blake match was over, Haas, a three-time champion in Memphis, had decided to step aside. He said his body ached and medication did not ease the symptoms.
"It's unfortunate," Haas said through ATP officials. "It never feels good to have to withdraw. This tournament has been good to me over the years, and it is disappointing."
Earlier in the women's quarterfinals, top-seeded Kirsten Flipkens of Belgium was eliminated by Magdalena Rybarikova of Slovakia, the No. 7 seed, 6-7 (11), 7-5, 6-3.
Flipkens' loss meant the tournament's top two seeds in the women's draw have been eliminated. Second-seeded Sofia Arvidsson lost her second-round match to Marina Erakovic on Wednesday.
And fourth-seeded Heather Watson of Britain also lost Thursday, 6-1, 6-2 to Stefanie Voegele of Switzerland.
That left Sabine Lisicki of Germany as the only player in the top half of the draw to move on to the semifinals after she defeated eighth-seeded Kristina Mladenovic 6-3, 6-3.
In Friday's semifinals, Voegele will play Erakovic of New Zealand, a 7-5, 6-2 winner over Jamie Hampton of the United States on Thursday, while Lisicki and Rybarikova will face off in the other match.