After the Cardiff City Stadium had paid tribute to missing Cardiff striker Emiliano Sala, Cherries goalkeeper Artur Boruc soon had to deny Oumar Niasse.
In the fifth minute, Reid put Cardiff ahead from the penalty spot, after Steve Cook handled Josh Murphy's cross.
Cardiff doubled their lead 15 seconds after the break. Aron Gunnarsson played in Reid, who rounded Boruc to tap in.
Nathan Ake headed a late chance wide for AFC Bournemouth, who remain 10th on 33 points.
A first win in five matches puts Cardiff on 22 points, two behind 17th-placed Burnley.
Cardiff: 9 Feb v Southampton (A)
AFC Bournemouth: 9 Feb v Liverpool (A)