World number 14 Kashyap could not quell the challenge from the 41st ranked Russian, losing 18-21 18-21 in the first men's singles at the Siri Fort Sports Complex.
However, Taipei's Tai Tzu stunned three-time All England Champion and 11th ranked Tine 21-17 21-18 in the women's singles match to level the tie 1-1.
Kashyap was leading in the first game and had a healthy 7-2 lead at the break but Vladimir turned the tables on him at the second interval, moving to 14-12.
In the second game, Kashyap played an attacking game and opened up a 7-2 lead at the first break but Vladimir made it 8-9 with some attaching stroke-play.
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Vladimir fought back brilliantly but the Indian was able to keep his nose ahead at 14-10.
Kashyap got points with his sharp angled smashes but he also committed few unforced errors as Vladimir kept breathing down his neck even after the break.
Kashyap lost a few points at the net and also failed to handle his rivals smashes to allow him to level par at 18-18.