"He played awesome in very windy conditions," head coach Robert Cox said. "He was down 5-4 in the third set and Klinger was serving for the match. Oggie broke his serve and then played a great tiebreaker."
Kolev, who improved to 27-13 with the victory, advances to Thursday's second round and will face Harsh Mankad of Minnesota. Mankad beat Tulane's Michael Kogan, 6-1, 7-6 (7-2), in the first round.
"Harsh is one of the best players in the country," Cox said. "He was ranked No. 1 in the fall. Oggie's win was incredible. It's a good win for the program and for Oggie."
Arkansas' last individual victory in NCAA Tournament play came in 2000 when Oskar Johansson beat Jeremy Bayon of Mississippi State, 6-2, 6-3, in the first round before falling in the second round.
Kolev is ranked No. 35 in the nation by the Intercollegiate Tennis Association while Mankad is No. 4.