World number seven Cilic failed to convert any of three set points in the opening set tiebreak against Serb Tipsarevic, but took four straight games from 2-2 in the second set to level.
He then broke early in the deciding set and held firm.
"It's never easy, especially the first match on grass," Cilic told the ATP's website. "Janko has been at the top of the tennis game and is a quality player."
Cilic will seek a 50th career grasscourt victory on Friday when he plays Canada's Vasek Pospisil, who was leading Alexandr Dolgopolov when his opponent retired.
"I'm playing way, way better than at the start of the year and my claycourt game helped me to get into the right hitting zone," said Cilic. "Having strong mental toughness, which you need on clay, also gives me confidence."
The 38-year-old Karlovic said he has been sharpening his lawn game for more than a week.
"It was good as I was here preparing here for the past seven days," he said. "I'm happy with the way I performed."
He will now play Russia's Daniil Medvedev, who beat fellow 21-year-old Thanasi Kokkinakis.
(Reporting by Martyn Herman; editing by Mark Heinrich)
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