Scarlets had three players sin-binned, but held on to claim only their second league victory this season in a game in which Cardiff dominated territory and possession.
Centre Eddie James crossed to give Scarlets the lead with Joe Hawkins adding the conversion.
Cardiff hit back to level through a try from Mason Grady after both Josh Macleod and Davies had been shown yellow cards.
Callum Sheedy nudged Cardiff ahead with a penalty just before the break, but Gareth Davies crossed twice, either side of a second try for the home side by Josh Adams.
Johnny Williams became the third Scarlets player to be yellow-carded with an hour gone, but high-flying Cardiff could not find a response.
“It wasn’t great for the nerves,” said Peel.
“Three yellow cards put us in a difficult position, but we fought hard.
“We took our opportunities when they came and I thought we fought splendidly well for each other. It was a great win.”
Former Wales scrum-half Davies, 35, scored two tries at the Arms Park for a third successive season.
“I can’t speak highly enough about him because he’s the ultimate professional and keeps himself in great shape,” said Peel.
“He said to me before the game he fancied another double so he backed that up.”