The enigmatic 29-year-old showed some nice touches at full-back as the Blues strangled the life out of their struggling opponents.
The win was enough to fire Henson and co into fourth in the RaboDirect PRO12, behind leaders Leinster and Welsh rivals the Ospreys and level with Munster.
First-half tries from winger Alex Cuthbert and second row Bradley Davies allowed the Blues to take a significant lead into the break.
And after kicking his side out of range of a comeback, Halfpenny produced a searing break to set up Cuthbert for his second to seal the win.
The Blues missed an early chance to take the lead as Halfpenny fluffed his first penalty attempt, but Jason Tovey missed an easy opportunity of his own to keep the game scoreless in the first quarter.
That changed when Cuthbert went over for the first try after a fantastic offload from kiwi centre Casey Laulala left him with a free run to the line.
Halfpenny converted before adding a penalty to give the home side a 10-0 lead after half an hour.
Tovey pulled three points back for the visitors but on the stroke of half-time Wales international Davies barged his way over after a period of relentless pressure from the home side eventually caused the Dragons defence to crack.
The visiting side defended valiantly against wave after wave of Blues pressure but the try had an air of inevitability about it as Davies went over, Halfpenny's conversion making it 17-3 at the break.
Tovey and Halfpenny exchanged penalties at the start of the second half, adding six points each to make it 23-9 with a quarter of an hour remaining.
And after playing a major part with the boot, Halfpenny showed his great pace and vision to tear through the Dragons defensive line before offloading for Cuthbert to race over for his second, Halfpenny's conversion finding the post.
There was more good news for the Blues as Jamie Roberts' knee injury which forced him off in the second half was less serious than initially thought.
|Cardiff Blues Score Card|
|Newport Gwent Dragons Score Card|