The Blues’ chances weren’t helped by yet another two yellow cards, including one to Craig Quinnell on his return from a six-week suspension, but Bowen did the damage with a faultless display of goal-kicking.
The Blues made the most of a strong wind in the opening half, but needed more than a four-point lead as they turned to play into it.
Bowen opened the scoring with a penalty goal, before opposite number Nick Robinson carved through the home defence to give lock Andy Moore a free run to the try-line. Robinson converted and took his side out to 10-3 when older brother Jamie was taken high by Scott Quinnell.
The visitors’ good start suffered a knock when impressive young flanker Robin Sowden-Taylor was sin-binned for killing the ball, but the Blues ignored their one-man deficit when winger Lee Abdul intercepted a Leigh Davies pass to score a 75-metre try.
From the next phase of play, Davies went from zero to hero by supplying a pass that put centre Matthew Watkins over the try-line as the Blues defenders were still celebrating Abdul’s try.
Robinson and Bowen traded penalty goals as the Blues went into the break with a 20-16 lead, which Bowen narrowed to a one-point margin with his fourth penalty goal.
Craig Quinnell was banished to the bin for a professional foul, and Bowen’s fifth penalty goal and 100th Celtic League point this season gave his side the lead for the first time since the opening minutes.
Scarlets winger and Wales sevens star Tal Selley confirmed the victory with a well-taken try in the 78th minute, dashing Cardiff hopes of a bonus point in the process.