JOIN USDevvarman, who turned pro a year ago, should have won the first set, having broken the Russian's service twice, but could not press home the advantage Tuesday.
Kunitsyn, who has not won consecutive matches since reaching the Memphis quarter-finals in February, took the second set comfortably and with it the match, though tennis bookies had favoured the Indian to win it over three sets.
For the 24-year-old Indian, twice NCAA singles champion, this was the second successive defeat against the Russian, having lost to the world number 37 in his first pro tournament, Legg Mason Tennis Classic, 4-6, 1-6, after winning his first career ATP match defeating Taylor Dent.
Devvarman, a graduate of the University of Virginia, slumped 25 ranks to 152 on ATP charts released Monday from a career-best 125 last week.
Kunitsyn next plays Argentinean Leonardo Mayer who beat French qualifier Josselin Ouanna 6-2, 6-3.
American John Isner fired 15 aces and dropped only four points on his first serve in clinching two tough tie-breakers to surprise seventh-seeded German Benjamin Becker 7-6(8), 7-6 (3) as he carried his form that took him into last week's Indianapolis semi-finals.
Isner, a 2007 NCAA finalist at Georgia Tech, improved to 3-0 head-to-head against Becker, the NCAA winner at Baylor in 2004. Isner started the week at a career-high ranking of 77.
Former Australian Open finalist and World No. 8 Marcos Baghdatis of Cyprus saved eight of nine break points he faced to defeat Indianpolis semi-finalist Frank Dancevic 7-6 (3), 6-3 to reach the second round, where he will play Isner.
The Cypriot, who is also a former Wimbledon semi-finalist, has slipped to No.146 on the ATP Rankings.
Baghdatis began the year strongly with a fourth-round showing at the Australian Open and a quarter-final appearance in Johannesburg, but he last won consecutive matches on the ATP World Tour back in February at Delray Beach, when he also reached the quarters.
In other first round matches, Latvian Ernests Gulbis, loser in eight of his last ten matches, beat Yen-Hsun Lu of Chinese Taipei 7-5, 6-2; Australian qualifier Carsten Ball beat Frenchman Marc Gicquel 6-2, 7-6 (6); and American qualifier Ryan Sweeting defeated compatriot Taylor Dent 6-4, 2-6, 6-3.