The Premier League leaders had broken the away side's resolve in the 33rd minute when Kai Havertz got on the end of a Reece James cross.
The Blues had ample opportunities to score either side of the German forward's finish, but were unable to find a way past Nick Pope.
And they became the victims of Burnley's smash and grab in the 79th minute as Vydra converted from close range.
The Czech Republic international coolly lifted the ball over Edouard Mendy after fellow substitute Jay Rodriguez had guided Ashley Westwood's whipped cross into his path.
It was the sixth point that Sean Dyche's side had collected from their last seven top flight trips to SW6.
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And they became the victims of Burnley's smash and grab in the 79th minute as Vydra converted from close range.