The Dragons hit back in perfect style after the break with Andy Tuilagi going over and Wayne Evans adding the conversion and a penalty to put his side in front.
But another Patchell penalty sealed derby glory for the Blues at Arms Park, the result moving Davies' men up to seventh in the RaboDirect PRO12 table.
It was the perfect response to back-to-back RaboDirect PRO12 defeats, the Blues falling 33-12 at Ospreys before a narrow 9-6 loss at home to the Scarlets last time out.
And after surviving five minutes of concerted pressure deep in their territory at the death with Lewis Robling hitting a drop goal wide, Davies maintained his players merited a bit of good fortune.
"I was so nervous for the players. Just the effort they have put in week-in, week-out has been brilliant and we've not got a lot of rewards at times," said Davies.
"It's been pretty painful with some results and to see them after the game was great.
"I couldn't watch the last five minutes. I don't know what's wrong with me.
"I'm flipping 50 next year! That's the first time I've been like that for a long time."
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