Wales international Vokes netted the winner on 70 minutes with a stooping header after Josh Murphy had levelled for the Bluebirds 10 minutes earlier with a stunning strike.
Icelandic international Berg Gudmundsson had opened the scoring on 51 minutes with a back-post header before setting up Vokes for the winner with a clipped pass.
The win lifted Sean Dyche's side up five places to 12th but left City rooted in 19th spot on just two points and still searching for their first win of the season.
But the Clarets suffered a blow on 27 minutes when England defender James Tarkowski was forced off with a shoulder injury to be replaced by Kevin Long.
The centre-back had picked up the injury on eight minutes when blocking a shot but carried on after treatment until it became too painful to continue.
But Tarkowski – who won his second cap for the Three Lions when starting the recent friendly in Switzerland – could now be a doubt to make Gareth Southgate's squad for the coming Nations League games against Croatia and Spain.
Cardiff created the best chances in the first-half with Murphy hitting the post from a tight angle on 18 minutes though Joe Hart looked to have the shot covered anyway.
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The England stopper was forced to make a smart save low down near his post on 35 minutes from Kenneth Zohore's toe-poked effort from Victor Camarasa's neat pass.
Murphy did head the ball into the net from the resulting corner but it was ruled out for City skipper Sean Morrison climbing all over Long to flick a header on.
Morrison did get a clean header five minutes later which Sam Vokes could only flick closer to his own goal.
But Callum Paterson's header was cleared off the line by Matej Vydra when the City midfielder had time to pick his spot.
Vydra had had the only real first-half effort for the visitors but fired well over from 25 yards. And strike partner Sam Vokes should have done better five minutes after the break when he was put clear, but tripped over his own feet in the box while being challenged by Morrison.
But within moments Sean Dyche's side made the breakthrough as Gudmundsson headed home at the back post from Ashley Westwood's cross following a quickly taken throw-in.
The Icelandic international outjumped left-back Greg Cunningham and squeezed the ball between Neil Etheridge and his near post for his first goal of the season.
City almost made an instant response but Camarasa fired a volley just over the bar.
But Murphy did level on 60 minutes with a stunning strike for his first goal since his £11million move from Norwich City in the summer.
Camarasa fed Bruno Manga who had broken into the box and the right-box put over a low cross that Murphy smacked first tie low into the corner to give Hart no chance.
Murphy was denied a second on 68 minutes by a splendid save from Hart who was having the sort of game that made him England's regular No 1 for so long.
But two minutes later Westwood freed Berg Gudmundsson down the left and his cross found Vokes who stooped to send the ball into the corner to make it back-to-back wins for Burnley in the league.
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