Karlovic served 25 aces and had 49 winners, while Berdych had eight aces and 28 winners. Neither player managed to break serve.
"It's really hard to play someone who serves that well," Berdych said. "It's hard to find my rhythm on the court."
Karlovic now leads Berdych 4-2 in head-to-head meetings. Berdych was the only top-10 player who did not win an ATP tour title in 2013.
Karlovic, a former top 15 player, finished the 2013 season ranked No. 77. He missed nearly two months in the spring when he became ill with spinal meningitis.
For Murray, it will be his first ATP singles match since having back surgery in September, although he teamed with Nenad Zimonjic of Serbia to defeat German pair Daniel Brands and Florian Mayer in the doubles on Monday.
"I feel like I have recovered well from it (surgery), but it's still a process," said Murray, who lost an exhibition match against Jo-Wilfried Tsonga in Abu Dhabi last week. "You know, I don't know exactly how I'm going to wake up tomorrow, but today was good in the match."