Cilic will next face eighth-seeded Spaniard Marcel Granollers, who beat Lucas Dlouhy of the Czech Republic 7-5, 2-6, 6-4.
Fifth-seeded Rainer Schuettler also advanced after beating fellow German Bjorn Phau 6-2, 7-5 and will face India's Somdev Devvarman, who stunned fourth-seeded Ivo Karlovic of Croatia 7-6 (4), 6-4.
Cilic, the highest seed left in the tournament after top-seeded Nikolay Davydenko pulled out with a heel injury and No. 2 Stanislas Wawrinka was knocked out in the opening round, broke Tipsarevic in the third game en route to winning the first set. Tipsarevic bounced back to dominate the second before Cilic regained his composure in the third, capitalizing on his opponent's errors to earn the decisive break in the ninth game.
"Janko started playing much better and got the mental advantage after breaking me early in the second set, while I went a bit down with too many errors,'' Cilic said. "I got my rhythm back and started serving well again in the third set, and that clinched the result for me.''
Schuettler, a 32-year-old veteran, broke Phau twice to win the first set and then rallied from a 5-2 deficit in the second to beat his training partner.
"We're good friends, have played each other often and even had a hit out this morning,'' said Schuettler, who was a finalist here in 1999.
The German, who was a semifinalist at last year's Wimbledon, said his main focus was "to stay healthy this season.''
"Last year was the first time I played without any major injuries,'' he said. "I'm one of the oldest players on the tour. I know I just have a few years left, so I want to make good use of my time.''
The 202nd-ranked Devvarman reached his first ATP semifinal after earning the match's only break in the 10th game of the second set.
The 23-year-old home favorite, who won NCAA collegiate titles in 2006 and '07 playing for the University of Virginia, was a wild-card entry for the tournament. He is the first Indian player to reach the semifinals of the event since Leander Paes in 1998.
"It was a huge mental game,'' Devvarman said. "I'm pleased at the manner in which I played my baseline game and managed to serve well. ... I saw Karlovic struggle. I was conscious of the fact that the heat would affect him more than in would bother me.''
The hard-serving Karlovic described his performance as "amazingly bad.''
"It was a horrible display as I just couldn't put the ball in court,'' Karlovic said. "I can't remember when I last played like this.''
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