The Croatian fired down 24 aces and saved two break points en route to a 7-6(7) 7-6(4) victory in one hour 46 minutes.
"It is hard to play someone who serves that well,” Berdych told the ATP World Tour official website.
“It is also difficult to find my rhythm. Ivo is not an opponent you appreciate playing early on. You never have your destiny in your hands. You are waiting to see what will happen. I now must look forward to matches in the doubles."
Eighth seed Fernando Verdasco had to save a flurry of break points as he moved into the second round with a 6-3 6-3 win over Italian Filippo Volandri while Frenchman Gael Monfils progressed with a 7-6 6-2 win over Colombian Santiago Giraldo.
It was bad news for Britain's Kyle Edmund in the Chennai Open as he fell to a 6-3 7-5 defeat to Canada's fifth seed Vasek Pospisil.
Day One Results (Qatar Open)
Tobias Kamke bt Malek Jaziri (W) 6-4 6-3
Lukasz Kubot bt Daniel Gimeno-Traver 6-4 6-3
Victor Hanescu bt Joao Sousa 6-3 6-2
Ivo Karlovic bt Tomas Berdych (4) 7-6(7) 7-6(4)
Day One Results (Chennai Open)
Vasek Pospisil bt Kyle Edmund 6-3 7-5
Dudi Sela bt Lukas Lacko 6-4 6-2
Jiri Vesely bt Jeevan Nedunchezhiyan 7-5 6-2
Lu Yen-Hsun bt Tim Smyczek 6-4 6-2