Former India Davis Cupper Prakash Amritraj, who is now ranked 515th in the World, also won his match but in a contrasting style winning 6-7 (4) 6-2 6-2 against Rufin Guillaume of France.
Somdev, who has gone through a rough patch after returning from injury as his ATP ranking has slipped to 663 from top-100 rank a couple of years back.
On paper, Somdev was no match for his 106th ranked Czech opponent but India's top singles player proved his fitness which is a positive sign ahead of country's Davis Cup tie against South Korea in Delhi.
Once he broke Hajek in the very first game of the match, he grew in confidence and then in his first service game fired three aces to rattle his opponent.
Steadily, he went about his task and upped the ante and got better with each service game. He broke Hajek in the ninth game for the lead.
Devvarman seemed to have prepared well to take on the load and equipped with booming forehand drives. The Indian, who served seven aces in all, saved two of three break points in each set.
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"It's my first match of the year and it feels great to have won it. It is always a pleasure playing in Chennai, the crowd support helped me immensely," Somdev said after the match.
"Coming back from injury after so many months, to win my first match of the season is a wonderful feeling. The next match is going to be tough since I'm playing a seeded player, but I'm feeling good and will go out there and do my best."